Computation of Fifth Degree of Spline Function Model by Using C++ Programming
|
|
|
- Judith Joseph
- 5 years ago
- Views:
Transcription
1 89 Computton o Ft Degree o plne Functon Model b Usng C Progrmmng Frdun K. Hml, Aln A. Abdull nd Knd M. Qdr Mtemtcs Dept, Unverst o ulmn, ulmn, IRAQ Mtemtcs Dept, Unverst o ulmn, ulmn, IRAQ Mtemtcs Dept, Unverst o ulmn, ulmn, IRAQ Abstrct In ts pper, new quntc splne metod developed or computng pproxmte soluton o derentl equtons. It s sown tt te present metod s o te order tree nd our dervtves nd gves pproxmtons wc re better. Te numercl result obtned b te present metod s been compred wt te exct soluton usng C progrmmng nd lso llustrte grpcll te pplcblt o te new metod. B gettng te dvntges o te mtemtcl buldng unctons lke pow (or power, exp (or exponentl, etc. re provded n C progrmmng lbrr, ll processng steps re done ecentl nd llustrted s Pseudocode model. Kewords: - Quntc splne, Derentl equtons, Buldng unctons, Pseudocode.. Introducton A metod or pproxmte solvng ntl vlue problems proposed or derentl equtons. In ct, ts metod s vrnt o te well-known metod o splne nterpolton consdered n [. A prncpl derence between consdertons n [ nd ours s tt, te new cse o lcunr nterpoltons wt oters boundr condtons. Ts metod enbles us to pproxmte te soluton s well s ts rst nd trd dervtves t ever pont o te rnge o ntegrton. We proved tt ts new metod gves better numercl results tn te prevous known results. In recent ers, Al-d nd Noor [,, Kl nd Noor [ nd Noor nd Al-d [, ve used suc tpes o penlt uncton n solvng clss o contct problems n elstct n conjuncton wt collocton, nte derence nd splne tecnques. Te generl ourt order ntl vlue problem consdered s o te orm g( x, < x < Wt te boundr condtons x, ( x, ( x nd ( x. ( ( n x x nd tt C ([, R Were, n (, nd tt s Lpsctz contnuous n, smlrl or te trd order,,, nd ntl vlue problems. Te m o ts pper s to construct new splne metod bsed on quntc splne uncton tt s polnoml prt nd to develop numercl metods or obtnng smoot pproxmtons or te soluton o te problem ( subject to te ntl condtons (.
2 9 Te exstence nd unqueness or splne uncton o degree ve wc nterpolte te lcunr dt (, s presented nd exmned n ecton, we derve te numercl metod nd brel dscuss ts error nlss teoretcll n ecton. Convergence nlss or second order, ourt order nd t order metods s estblsed n ecton. Numercl results re presented to llustrte te pplcblt nd ccurc ter prctcl useulness wt C progrmmng n ecton. One o te C progrmmng powerul ncludes (cmt eder le. Te cmt eder le provdes collecton o unctons tt enbles progrmmer to perorm common mtemtcl clcultons [7. Te nstructons (codesre llustrted n Pseudocode. Pseudocode s compct nd norml g-level descrpton o computer progrmmng lgortm tt uses te structurl conventons o progrmmng lnguge, but t s ntended or umn redng rter tn mcne redng [8.. Explnton o te Metod We consder mes wt nodl ponts te x on [, b suc tt; : x < x <.. < x < x b were. x j x j (x n n, j,,,..., n. Also we denote quntc splne uncton, nterpoltng to uncton (x dened on [, b s suc tt: ( x x ( x x (! ( x x, ( x x, ( x x, ( x, ( x On te lst ntervl [ n, xn ollows: ( x nd x we dene ( j x n s n n ( x x ( x x ( x xn n, ( x x n n n, n, n n, ( x x! n ( n Were n, j, j,, nd, unknowns re to be determned. Teorem : Exstence nd Unqueness plne Model ( r Gves te rel numbers ( x,,,,, n nd r,, nd x nd ( x ten te exst unque ( n splne uncton o degree sx rom equtons (-( suc tt: ( x ( x ( r ( r ( x ( x, r, nd ( x ( x nd ( x ( x n n or,,..., n ( ( Proo: For wole ntervl x, x were,,,..., n [. Assumng (x to be te exct soluton o te equton (, obtned b te splne (x, long wt te contnut condton o te rst nd trd dervtves t [x -, x derved: n, te ollowng consstenc reltons re,,,,,,,, olvng te bove sstem, te coecents o (x on te ntervl [x,x or,,,..., n., ( ( 7 ( 8, ( ( ( 7 8 (7 (8
3 9, ( ( ( B solvng tese equtons, we see tt te coecents n, (9 ;, nd re unquel determned, snce we ve tree equtons nd tree unknowns, nd nll, we cn nd te coecents o ( smlrl n x n te ntervl [x n-,x n. Hence te proo s complete.. Convergence nlss In ts secton, we nvestgte te convergence nlss o te quntc splne metod descrbed n ecton.for ts purpose, te error bound o te splne uncton (x wc s soluton o te problem (nd s obtned or te unorm prtton I b te ollowng teorem: Teorem : Let C [, s te exct soluton o te derentl equtons (nd (x be unque splne uncton o degree ve wc soluton o te problem ( nd. Ten or x x, x ;,,,, n-, we ve ( r ( r [ r W ( r W ( r W ( r W ( 9 r W ( 7 W ( or or r r or r or r or r or r were W ( denotes te modules o contnut o (, dened b W mx{ W ; x } ( Proo: Let x x, x were,,, n-. [ From equton nd te Tlor s expnson ormul, we ve (, ( (, [ ( ( 7 ( ( [ ( [ ( 7 W (,, ( x x, 7 ( ( x x, ( 9 ( W (,, ( x x, ( x x, ( (, ( x x ( x x ( x x W (, ( x ( x x ( x x,,, ( W (, ( x x ( x x, ( x x! ( x x ( ( x x ( x x ( ( W (,,,,, ( x x! ( (
4 9 W (, Ts proves Teorem or x x, x, smlrl we cn ( [ obtn te result or x x n, x. Ts completes te proo. [ n. Illustrton Exmples: Ts secton, severl numercl exmples re gven to llustrte te propertes o te metod nd ll o tem were perormed on te computer usng progrm wrtten n [7, 8. Te bsolute errors n Tbles re te vlues o (x - t selected ponts, nd lso te ollowng gures re sown tt ncreses o te order dervtves ncreses te errors. Problem : we consder te ntl vlue problem were x [,, ( ( ( ( ( (, clerl tt, te exct soluton s x e. Te Pseudocode o problem s: or ( strt pont to end pont, ncrese strt pont b or ec step { tep : Fnd (* ((pow(,/* ((pow(, /* ( ((pow(,/* (* ((pow(,/* ( ( ( ((pow(,/* ( (,/* ( ((pow(,/* ( (* ( ((pow ( ( ((pow(,/* (/pow(,*( (/(**(7* (* (/*(* -* ( (/pow(,*( - - (/pow(,*( (/(**(7* * ( ( (/pow(,*( - - (/pow(,*( (/pow(,*( ( tep : Fnd (.*((exp(exp(- ( (.*(exp(- exp(- tep : Fnd Error - Error - Error ( - ( tep : Prnt Error, Error, Error respectvel. } Problem : Consder tt te t order boundr vlue problem ( were x [,, ( ( ( ( nd ( x x e e cos( x soluton s Te Pseudocode o problem s: te exct or ( strt pont to end pont, ncrese strt pont b or ec step { tep : Fnd ( ( tep : Fnd
5 9 (* ((pow(,/* ((pow(, /* ( ((pow(,/* ( ((pow(,/ * (* ( ( ((pow(,/* ( (,/* ( ((pow(,/* ( ( * ( * ( ( ((pow ( ( ((pow(, / Tble (: Mxmum errors n soluton o problem ( E E. -. * 9.9 *. -. *.8 * *.9 * ( E 9. * 9.9 *. * Tble (: Mxmum errors n soluton o problem ( E E *.87 *. - *.9 *. - *. * ( E 9.89 *.88 *. * tep : Fnd (/pow(,*(- Te ollowng gures observe te numercl results wt respect two orders o dervtve: (/(**(7* (* (/*(* - * ( (/pow(,*( - - (/pow(,*( (/(**(7* * ( Absolute Error Grp or problem, wen. Error Error Error Exct Exct Exct ( (/pow(,*( - - (/pow(,*( ( tep : Fnd exp(- ( -(exp(- tep : Fnd Error - Error - Error ( - (/pow(,*( ( tep : Prnt Error, Error, Error respectvel. }.E.E.E.E.E.E-.E Absolute Error Grp or problem, wen..97 Error Error Error Exct Exct Exct
6 9 It s observed tt te metod s te best dvntge wen.e.e.e.e.e.e-.e..... Absolute Error Grp or problem, wen Error Error Error Exct Exct Exct Error Error Error Exct Exct Exct te known unctons n equton cn be expnded to Tlor seres wt converge rpdl. In order to get te best pproxmton, we tke more terms rom te Tlor expnson o unctons; tt s, te truncton lmt N must be cosen lrge enoug. On te oter nd, rom Tble, t m be observed tt te solutons ound or derent sow close greement or vrous vlues o x. In prtculr, our results n tbles re usull better tn te oter metods, re sown n te bove gures. Anoter consderble dvntge o te metod s tt Tlor coecents o te soluton re ound ver esl b usng te computer progrms. - Absolute Error Grp or problem, wen.. Error Error. Error Exct Exct -. Exct Absolute Error Grp or problem, wen Error Error Error Ecxt Exct Exct Absolute Error Grp or problem, wen.. Dscusson: A new tecnque, usng te Tlor seres, to numercll soluton te pntogrp equtons s presented. Reerences [ Abbs Y. Al Bt, Rostm K. eed nd Frdun K. Hm- l (9 Te Exstence, Unqueness nd Error Bounds o Approxmton plnes Interpolton or olvng econd-order Intl Vlue Problems, Journl o Mtemtcs nd ttstcs (:-9,, IN 9-. [ E.A. Al-d, M.A. Noor, Computtonl metods or ourtorder obstcle boundr vlue problems, Comm. Appl. Nonlner Anl. ( [ E.A. Al-d, M.A. Noor, Qurtc splne metod or solvng ourt-order obstcle boundr vlue problems, J. Comput. Appl. Mt. ( 7. [ A.K. Kl, M.A. Noor, Quntc splnes solutons o clss o contct problems, Mt. Comput. Modell. (99 8. [ M.A. Noor, E.A. Al-d, Fourt-order obstcle problems, n: T.M. Rsss, H.M. rvstv (Eds., Anltc nd Geometrc Inequltes nd Applctons, Kluwer Acdemc Publsers, Dordrect, Hollnd, 999, pp. 77. [ M.A. Noor, E.A. Al-d, Numercl solutons o ourt-order vrtonl nequltes, Int. J. Comput. Mt. 7 ( 7. [7 P.J. DEITEL, H.M. DEITEL, How To Progrm C, xt Edton,8. [8 Y. Dnel Lng, Introducton to Progrmmng Wt C, 7.
ORDINARY DIFFERENTIAL EQUATIONS
6 ORDINARY DIFFERENTIAL EQUATIONS Introducton Runge-Kutt Metods Mult-step Metods Sstem o Equtons Boundr Vlue Problems Crcterstc Vlue Problems Cpter 6 Ordnr Derentl Equtons / 6. Introducton In mn engneerng
Chapter Runge-Kutta 2nd Order Method for Ordinary Differential Equations
Cter. Runge-Kutt nd Order Metod or Ordnr Derentl Eutons Ater redng ts cter ou sould be ble to:. understnd te Runge-Kutt nd order metod or ordnr derentl eutons nd ow to use t to solve roblems. Wt s te Runge-Kutt
ORDINARY DIFFERENTIAL EQUATIONS EULER S METHOD
Numercal Analss or Engneers German Jordanan Unverst ORDINARY DIFFERENTIAL EQUATIONS We wll eplore several metods o solvng rst order ordnar derental equatons (ODEs and we wll sow ow tese metods can be appled
International Journal of Pure and Applied Sciences and Technology
Int. J. Pure Appl. Sc. Technol., () (), pp. 44-49 Interntonl Journl of Pure nd Appled Scences nd Technolog ISSN 9-67 Avlle onlne t www.jopst.n Reserch Pper Numercl Soluton for Non-Lner Fredholm Integrl
Chapter Newton-Raphson Method of Solving a Nonlinear Equation
Chpter 0.04 Newton-Rphson Method o Solvng Nonlner Equton Ater redng ths chpter, you should be ble to:. derve the Newton-Rphson method ormul,. develop the lgorthm o the Newton-Rphson method,. use the Newton-Rphson
Lecture 4: Piecewise Cubic Interpolation
Lecture notes on Vrtonl nd Approxmte Methods n Appled Mthemtcs - A Perce UBC Lecture 4: Pecewse Cubc Interpolton Compled 6 August 7 In ths lecture we consder pecewse cubc nterpolton n whch cubc polynoml
4. Eccentric axial loading, cross-section core
. Eccentrc xl lodng, cross-secton core Introducton We re strtng to consder more generl cse when the xl force nd bxl bendng ct smultneousl n the cross-secton of the br. B vrtue of Snt-Vennt s prncple we
Introduction to Numerical Integration Part II
Introducton to umercl Integrton Prt II CS 75/Mth 75 Brn T. Smth, UM, CS Dept. Sprng, 998 4/9/998 qud_ Intro to Gussn Qudrture s eore, the generl tretment chnges the ntegrton prolem to ndng the ntegrl w
INTERPOLATION(1) ELM1222 Numerical Analysis. ELM1222 Numerical Analysis Dr Muharrem Mercimek
ELM Numercl Anlss Dr Muhrrem Mercmek INTEPOLATION ELM Numercl Anlss Some of the contents re dopted from Lurene V. Fusett, Appled Numercl Anlss usng MATLAB. Prentce Hll Inc., 999 ELM Numercl Anlss Dr Muhrrem
, rst we solve te PDE's L ad L ad n g g (x) = ; = ; ; ; n () (x) = () Ten, we nd te uncton (x), te lnearzng eedbac and coordnates transormaton are gve
Freedom n Coordnates Transormaton or Exact Lnearzaton and ts Applcaton to Transent Beavor Improvement Kenj Fujmoto and Tosaru Suge Dvson o Appled Systems Scence, Kyoto Unversty, Uj, Kyoto, Japan suge@robotuassyoto-uacjp
ME 501A Seminar in Engineering Analysis Page 1
More oundr-vlue Prolems nd genvlue Prolems n Os ovemer 9, 7 More oundr-vlue Prolems nd genvlue Prolems n Os Lrr retto Menl ngneerng 5 Semnr n ngneerng nlss ovemer 9, 7 Outlne Revew oundr-vlue prolems Soot
LOCAL FRACTIONAL LAPLACE SERIES EXPANSION METHOD FOR DIFFUSION EQUATION ARISING IN FRACTAL HEAT TRANSFER
Yn, S.-P.: Locl Frctonl Lplce Seres Expnson Method for Dffuson THERMAL SCIENCE, Yer 25, Vol. 9, Suppl., pp. S3-S35 S3 LOCAL FRACTIONAL LAPLACE SERIES EXPANSION METHOD FOR DIFFUSION EQUATION ARISING IN
THE COMBINED SHEPARD ABEL GONCHAROV UNIVARIATE OPERATOR
REVUE D ANALYSE NUMÉRIQUE ET DE THÉORIE DE L APPROXIMATION Tome 32, N o 1, 2003, pp 11 20 THE COMBINED SHEPARD ABEL GONCHAROV UNIVARIATE OPERATOR TEODORA CĂTINAŞ Abstrct We extend the Sheprd opertor by
CENTROID (AĞIRLIK MERKEZİ )
CENTOD (ĞLK MEKEZİ ) centrod s geometrcl concept rsng from prllel forces. Tus, onl prllel forces possess centrod. Centrod s tougt of s te pont were te wole wegt of pscl od or sstem of prtcles s lumped.
Chapter Newton-Raphson Method of Solving a Nonlinear Equation
Chpter.4 Newton-Rphson Method of Solvng Nonlner Equton After redng ths chpter, you should be ble to:. derve the Newton-Rphson method formul,. develop the lgorthm of the Newton-Rphson method,. use the Newton-Rphson
TR/95 February Splines G. H. BEHFOROOZ* & N. PAPAMICHAEL
TR/9 February 980 End Condtons for Interpolatory Quntc Splnes by G. H. BEHFOROOZ* & N. PAPAMICHAEL *Present address: Dept of Matematcs Unversty of Tabrz Tabrz Iran. W9609 A B S T R A C T Accurate end condtons
LAPLACE TRANSFORM SOLUTION OF THE PROBLEM OF TIME-FRACTIONAL HEAT CONDUCTION IN A TWO-LAYERED SLAB
Journl of Appled Mthemtcs nd Computtonl Mechncs 5, 4(4), 5-3 www.mcm.pcz.pl p-issn 99-9965 DOI:.75/jmcm.5.4. e-issn 353-588 LAPLACE TRANSFORM SOLUTION OF THE PROBLEM OF TIME-FRACTIONAL HEAT CONDUCTION
Applied Statistics Qualifier Examination
Appled Sttstcs Qulfer Exmnton Qul_june_8 Fll 8 Instructons: () The exmnton contns 4 Questons. You re to nswer 3 out of 4 of them. () You my use ny books nd clss notes tht you mght fnd helpful n solvng
CISE 301: Numerical Methods Lecture 5, Topic 4 Least Squares, Curve Fitting
CISE 3: umercl Methods Lecture 5 Topc 4 Lest Squres Curve Fttng Dr. Amr Khouh Term Red Chpter 7 of the tetoo c Khouh CISE3_Topc4_Lest Squre Motvton Gven set of epermentl dt 3 5. 5.9 6.3 The reltonshp etween
APPROXIMATE SOLUTION OF HIGHER ORDER LINEAR DIFFERENTIAL EQUATIONS BY MEANS OF A NEW RATIONAL CHEBYSHEV COLLOCATION METHOD
thetcl nd oputtonl Applctons ol. 5 o. pp. 5-56. Assocton for Scentfc eserch APPOXIAE SOLUIO OF HIGHE ODE LIEA DIFFEEIAL EQUAIOS BY EAS OF A EW AIOAL HEBYSHE OLLOAIO EHOD Slh Ylçınbş * esrn Özso ehet Sezer
7.2 Volume. A cross section is the shape we get when cutting straight through an object.
7. Volume Let s revew the volume of smple sold, cylnder frst. Cylnder s volume=se re heght. As llustrted n Fgure (). Fgure ( nd (c) re specl cylnders. Fgure () s rght crculr cylnder. Fgure (c) s ox. A
Jens Siebel (University of Applied Sciences Kaiserslautern) An Interactive Introduction to Complex Numbers
Jens Sebel (Unversty of Appled Scences Kserslutern) An Interctve Introducton to Complex Numbers 1. Introducton We know tht some polynoml equtons do not hve ny solutons on R/. Exmple 1.1: Solve x + 1= for
Initial Imperfections of Steel and Steel-Concrete Circular Columns
Recent dvnces n Contnuum echncs, Hdrolog nd colog Intl Imperectons o Steel nd Steel-Conete Crculr Columns RCL KRZÍOVÁ nd JIDRICH LCHR Fcult o Cvl ngneerng Brno Unverst o Technolog Veveří St. 33/95, 6 Brno
DCDM BUSINESS SCHOOL NUMERICAL METHODS (COS 233-8) Solutions to Assignment 3. x f(x)
DCDM BUSINESS SCHOOL NUMEICAL METHODS (COS -8) Solutons to Assgnment Queston Consder the followng dt: 5 f() 8 7 5 () Set up dfference tble through fourth dfferences. (b) Wht s the mnmum degree tht n nterpoltng
Pyramid Algorithms for Barycentric Rational Interpolation
Pyrmd Algorthms for Brycentrc Rtonl Interpolton K Hormnn Scott Schefer Astrct We present new perspectve on the Floter Hormnn nterpolnt. Ths nterpolnt s rtonl of degree (n, d), reproduces polynomls of degree
On generalized 2-step continuous linear multistep method of hybrid type for the integration of second order ordinary differential equations
Avlble onlne t www.colrreerclbrry.co Scolr Reerc brry Arcve o Apple Scence Reerc :- ttp://colrreerclbrry.co/rcve.tl ISSN 9-X CODEN USA AASRC9 On generlze -tep contnuou lner ulttep eto o ybr type or te
Model Fitting and Robust Regression Methods
Dertment o Comuter Engneerng Unverst o Clorn t Snt Cruz Model Fttng nd Robust Regresson Methods CMPE 64: Imge Anlss nd Comuter Vson H o Fttng lnes nd ellses to mge dt Dertment o Comuter Engneerng Unverst
On a nonlinear compactness lemma in L p (0, T ; B).
On a nonlnear compactness lemma n L p (, T ; B). Emmanuel Matre Laboratore de Matématques et Applcatons Unversté de Haute-Alsace 4, rue des Frères Lumère 6893 Mulouse E.Matre@ua.fr 3t February 22 Abstract
Lecture Note 4: Numerical differentiation and integration. Xiaoqun Zhang Shanghai Jiao Tong University
Lecture Note 4: Numericl differentition nd integrtion Xioqun Zng Sngi Jio Tong University Lst updted: November, 0 Numericl Anlysis. Numericl differentition.. Introduction Find n pproximtion of f (x 0 ),
Math 497C Sep 17, Curves and Surfaces Fall 2004, PSU
Mth 497C Sep 17, 004 1 Curves nd Surfces Fll 004, PSU Lecture Notes 3 1.8 The generl defnton of curvture; Fox-Mlnor s Theorem Let α: [, b] R n be curve nd P = {t 0,...,t n } be prtton of [, b], then the
The Number of Rows which Equal Certain Row
Interntonl Journl of Algebr, Vol 5, 011, no 30, 1481-1488 he Number of Rows whch Equl Certn Row Ahmd Hbl Deprtment of mthemtcs Fcult of Scences Dmscus unverst Dmscus, Sr hblhmd1@gmlcom Abstrct Let be X
Solution for singularly perturbed problems via cubic spline in tension
ISSN 76-769 England UK Journal of Informaton and Computng Scence Vol. No. 06 pp.6-69 Soluton for sngularly perturbed problems va cubc splne n tenson K. Aruna A. S. V. Rav Kant Flud Dynamcs Dvson Scool
OPTIMISATION. Introduction Single Variable Unconstrained Optimisation Multivariable Unconstrained Optimisation Linear Programming
OPTIMIATION Introducton ngle Varable Unconstraned Optmsaton Multvarable Unconstraned Optmsaton Lnear Programmng Chapter Optmsaton /. Introducton In an engneerng analss, sometmes etremtes, ether mnmum or
Stanford University CS254: Computational Complexity Notes 7 Luca Trevisan January 29, Notes for Lecture 7
Stanford Unversty CS54: Computatonal Complexty Notes 7 Luca Trevsan January 9, 014 Notes for Lecture 7 1 Approxmate Countng wt an N oracle We complete te proof of te followng result: Teorem 1 For every
90 S.S. Drgomr nd (t b)du(t) =u()(b ) u(t)dt: If we dd the bove two equltes, we get (.) u()(b ) u(t)dt = p(; t)du(t) where p(; t) := for ll ; t [; b]:
![90 S.S. Drgomr nd (t b)du(t) =u()(b ) u(t)dt: If we dd the bove two equltes, we get (.) u()(b ) u(t)dt = p(; t)du(t) where p(; t) := for ll ; t [; b]:](/thumbs/77/75155737.jpg "90 S.S. Drgomr nd (t b)du(t) =u()(b ) u(t)dt: If we dd the bove two equltes, we get (.) u()(b ) u(t)dt = p(; t)du(t) where p(; t) := for ll ; t [; b]:")
RGMIA Reserch Report Collecton, Vol., No. 1, 1999 http://sc.vu.edu.u/οrgm ON THE OSTROWSKI INTEGRAL INEQUALITY FOR LIPSCHITZIAN MAPPINGS AND APPLICATIONS S.S. Drgomr Abstrct. A generlzton of Ostrowsk's
INSTITUTE OF AERONAUTICAL ENGINEERING Dundigal, Hyderabad
INSTITUTE OF AERONAUTICAL ENGINEERING Dundgl, Hyderbd - 5 3 FRESHMAN ENGINEERING TUTORIAL QUESTION BANK Nme : MATHEMATICS II Code : A6 Clss : II B. Te II Semester Brn : FRESHMAN ENGINEERING Yer : 5 Fulty
NUMERICAL MODELLING OF TWO-DIMENSIONAL HEAVE FOR SLABS- ON-GROUND AND SHALLOW FOUNDATIONS
56 TH CANADIAN GEOTECHNICAL CONFERENCE 4 TH JOINT IAH-CNC/CGS CONFERENCE 2003 NAGS CONFERENCE 56 ème CONFÉRENCE CANADIENNE DE GÉOTECHNIQUE 4 ème CONFÉRENCE CONJOINTE AIH-CCN/SCG 2003 NAGS CONFÉRENCE NUMERICAL
Some Unbiased Classes of Estimators of Finite Population Mean
Itertol Jourl O Mtemtcs Ad ttstcs Iveto (IJMI) E-IN: 3 4767 P-IN: 3-4759 Www.Ijms.Org Volume Issue 09 etember. 04 PP-3-37 ome Ubsed lsses o Estmtors o Fte Poulto Me Prvee Kumr Msr d s Bus. Dertmet o ttstcs,
Endogenous timing in a mixed oligopoly consisting of a single public firm and foreign competitors. Abstract
Endogenous tmng n a mxed olgopoly consstng o a sngle publc rm and oregn compettors Yuanzhu Lu Chna Economcs and Management Academy, Central Unversty o Fnance and Economcs Abstract We nvestgate endogenous
The Karush-Kuhn-Tucker. Nuno Vasconcelos ECE Department, UCSD
e Karus-Kun-ucker condtons and dualt Nuno Vasconcelos ECE Department, UCSD Optmzaton goal: nd mamum or mnmum o a uncton Denton: gven unctons, g, 1,...,k and, 1,...m dened on some doman Ω R n mn w, w Ω
Chapter 3 Differentiation and Integration
MEE07 Computer Modelng Technques n Engneerng Chapter Derentaton and Integraton Reerence: An Introducton to Numercal Computatons, nd edton, S. yakowtz and F. zdarovsky, Mawell/Macmllan, 990. Derentaton
Stratified Extreme Ranked Set Sample With Application To Ratio Estimators
Journl of Modern Appled Sttstcl Metods Volume 3 Issue Artcle 5--004 Strtfed Extreme Rned Set Smple Wt Applcton To Rto Estmtors Hn M. Smw Sultn Qboos Unversty, smw@squ.edu.om t J. Sed Sultn Qboos Unversty
Lecture 36. Finite Element Methods
CE 60: Numercl Methods Lecture 36 Fnte Element Methods Course Coordntor: Dr. Suresh A. Krth, Assocte Professor, Deprtment of Cvl Engneerng, IIT Guwht. In the lst clss, we dscussed on the ppromte methods
Math Week 5 concepts and homework, due Friday February 10
Mt 2280-00 Week 5 concepts nd omework, due Fridy Februry 0 Recll tt ll problems re good for seeing if you cn work wit te underlying concepts; tt te underlined problems re to be nded in; nd tt te Fridy
Finite Difference Method
7/0/07 Instructor r. Ramond Rump (9) 747 698 rcrump@utep.edu EE 337 Computatonal Electromagnetcs (CEM) Lecture #0 Fnte erence Method Lecture 0 These notes ma contan coprghted materal obtaned under ar use
Point-based methods for estimating the length of a parametric curve
Journl of Computtonl nd Appled Mthemtcs 196 (006) 51 5 www.elsever.com/locte/cm Pont-bsed methods for estmtng the length of prmetrc curve Mchel S. Floter, Atgerr F. Rsmussen CMA, Unversty of Oslo, P.O.
Katholieke Universiteit Leuven Department of Computer Science
Updte Rules for Weghted Non-negtve FH*G Fctorzton Peter Peers Phlp Dutré Report CW 440, Aprl 006 Ktholeke Unverstet Leuven Deprtment of Computer Scence Celestjnenln 00A B-3001 Heverlee (Belgum) Updte Rules
Rank One Update And the Google Matrix by Al Bernstein Signal Science, LLC
Introducton Rnk One Updte And the Google Mtrx y Al Bernsten Sgnl Scence, LLC www.sgnlscence.net here re two dfferent wys to perform mtrx multplctons. he frst uses dot product formulton nd the second uses
Name: SID: Discussion Session:
Nme: SID: Dscusson Sesson: hemcl Engneerng hermodynmcs -- Fll 008 uesdy, Octoer, 008 Merm I - 70 mnutes 00 onts otl losed Book nd Notes (5 ponts). onsder n del gs wth constnt het cpctes. Indcte whether
Math 324 Advanced Financial Mathematics Spring 2008 Final Exam Solutions May 2, 2008
Mat 324 Advanced Fnancal Matematcs Sprng 28 Fnal Exam Solutons May 2, 28 Ts s an open book take-ome exam. You may work wt textbooks and notes but do not consult any oter person. Sow all of your work and
UNIVERSITY OF IOANNINA DEPARTMENT OF ECONOMICS. M.Sc. in Economics MICROECONOMIC THEORY I. Problem Set II
Mcroeconomc Theory I UNIVERSITY OF IOANNINA DEPARTMENT OF ECONOMICS MSc n Economcs MICROECONOMIC THEORY I Techng: A Lptns (Note: The number of ndctes exercse s dffculty level) ()True or flse? If V( y )
Differential Entropy 吳家麟教授
Deretl Etropy 吳家麟教授 Deto Let be rdom vrble wt cumultve dstrbuto ucto I F s cotuous te r.v. s sd to be cotuous. Let = F we te dervtve s deed. I te s clled te pd or. Te set were > 0 s clled te support set
Topic 6b Finite Difference Approximations
/8/8 Course Instructor Dr. Rymond C. Rump Oice: A 7 Pone: (95) 747 6958 E Mil: rcrump@utep.edu Topic 6b Finite Dierence Approximtions EE 486/5 Computtionl Metods in EE Outline Wt re inite dierence pproximtions?
Study of Trapezoidal Fuzzy Linear System of Equations S. M. Bargir 1, *, M. S. Bapat 2, J. D. Yadav 3 1
mercn Interntonl Journl of Reserch n cence Technology Engneerng & Mthemtcs vlble onlne t http://wwwsrnet IN (Prnt: 38-349 IN (Onlne: 38-3580 IN (CD-ROM: 38-369 IJRTEM s refereed ndexed peer-revewed multdscplnry
Two Coefficients of the Dyson Product
Two Coeffcents of the Dyson Product rxv:07.460v mth.co 7 Nov 007 Lun Lv, Guoce Xn, nd Yue Zhou 3,,3 Center for Combntorcs, LPMC TJKLC Nnk Unversty, Tnjn 30007, P.R. Chn lvlun@cfc.nnk.edu.cn gn@nnk.edu.cn
EE 330 Lecture 24. Small Signal Analysis Small Signal Analysis of BJT Amplifier
EE 0 Lecture 4 Small Sgnal Analss Small Sgnal Analss o BJT Ampler Eam Frda March 9 Eam Frda Aprl Revew Sesson or Eam : 6:00 p.m. on Thursda March 8 n Room Sweene 6 Revew rom Last Lecture Comparson o Gans
FORMULAE FOR FINITE DIFFERENCE APPROXIMATIONS, QUADRATURE AND LINEAR MULTISTEP METHODS
Jourl o Mtemtcl Sceces: Advces d Alctos Volume Number - Pges -9 FRMULAE FR FINITE DIFFERENCE APPRXIMATINS QUADRATURE AND LINEAR MULTISTEP METHDS RAMESH KUMAR MUTHUMALAI Dertmet o Mtemtcs D G Vsv College
University of Washington Department of Chemistry Chemistry 452/456 Summer Quarter 2014
Lecture 16 8/4/14 Unversty o Washngton Department o Chemstry Chemstry 452/456 Summer Quarter 214. Real Vapors and Fugacty Henry s Law accounts or the propertes o extremely dlute soluton. s shown n Fgure
The Finite Element Method: A Short Introduction
Te Fnte Element Metod: A Sort ntroducton Wat s FEM? Te Fnte Element Metod (FEM) ntroduced by engneers n late 50 s and 60 s s a numercal tecnque for solvng problems wc are descrbed by Ordnary Dfferental
ON SIMPSON S INEQUALITY AND APPLICATIONS. 1. Introduction The following inequality is well known in the literature as Simpson s inequality : 2 1 f (4)
ON SIMPSON S INEQUALITY AND APPLICATIONS SS DRAGOMIR, RP AGARWAL, AND P CERONE Abstrct New neultes of Smpson type nd ther pplcton to udrture formule n Numercl Anlyss re gven Introducton The followng neulty
consider in the case of 1) internal resonance ω 2ω and 2) external resonance Ω ω and small damping
consder n the cse o nternl resonnce nd externl resonnce Ω nd smll dmpng recll rom "Two_Degs_Frdm_.ppt" tht θ + μ θ + θ = θφ + cos Ω t + τ where = k α α nd φ + μ φ + φ = θ + cos Ω t where = α τ s constnt
A Simple Research of Divisor Graphs
The 29th Workshop on Combnatoral Mathematcs and Computaton Theory A Smple Research o Dvsor Graphs Yu-png Tsao General Educaton Center Chna Unversty o Technology Tape Tawan yp-tsao@cuteedutw Tape Tawan
Numerical Solution of Linear Fredholm Fuzzy Integral Equations by Modified Homotopy Perturbation Method
Austrln Journl of Bsc nd Appled Scences, 4(): 646-643, ISS 99-878 umercl Soluton of Lner Fredholm Fuzzy Integrl Equtons y Modfed Homotopy Perturton Method S.M. Khorsn Ksr, M. Khezerloo, 3 M.H. Dogn Aghcheghloo
Spring Force and Power
Lecture 13 Chapter 9 Sprng Force and Power Yeah, energy s better than orces. What s net? Course webste: http://aculty.uml.edu/andry_danylov/teachng/physcsi IN THIS CHAPTER, you wll learn how to solve problems
A Spline based computational simulations for solving selfadjoint singularly perturbed two-point boundary value problems
ISSN 746-769 England UK Journal of Informaton and Computng Scence Vol. 7 No. 4 pp. 33-34 A Splne based computatonal smulatons for solvng selfadjont sngularly perturbed two-pont boundary value problems
Mixed Type Duality for Multiobjective Variational Problems
Ž. ournl of Mthemtcl Anlyss nd Applctons 252, 571 586 2000 do:10.1006 m.2000.7000, vlle onlne t http: www.delrry.com on Mxed Type Dulty for Multoectve Vrtonl Prolems R. N. Mukheree nd Ch. Purnchndr Ro
Key words. Numerical quadrature, piecewise polynomial, convergence rate, trapezoidal rule, midpoint rule, Simpson s rule, spectral accuracy.
O SPECTRA ACCURACY OF QUADRATURE FORMUAE BASED O PIECEWISE POYOMIA ITERPOATIO A KURGAOV AD S TSYKOV Abstrct It is well-known tt te trpezoidl rule, wile being only second-order ccurte in generl, improves
The Schur-Cohn Algorithm
Modelng, Estmton nd Otml Flterng n Sgnl Processng Mohmed Njm Coyrght 8, ISTE Ltd. Aendx F The Schur-Cohn Algorthm In ths endx, our m s to resent the Schur-Cohn lgorthm [] whch s often used s crteron for
Logarithms and Exponential Functions. Gerda de Vries & John S. Macnab. match as necessary, or to work these results into other lessons.
Logritms nd Eponentil Functions Gerd de Vries & Jon S. Mcn It is epected tt students re lred fmilir wit tis mteril. We include it ere for completeness. Te tree lessons given ere re ver sort. Te tecer is
Weighted Compact and Noncompact Scheme for Shock Tube and Shock Entropy Interaction
Wegted ompct nd Noncompct ceme or oc Tube nd oc Entropy Intercton Peng Xe oqun Lu Tecncl Report 7- ttp://www.ut.edu/mt/preprnt/ Wegted ompct nd Non-compct ceme or oc Tube nd oc Entropy Intercton Peng Xe
Numerical Simulation of One-Dimensional Wave Equation by Non-Polynomial Quintic Spline
IOSR Journal of Matematcs (IOSR-JM) e-issn: 78-578, p-issn: 319-765X. Volume 14, Issue 6 Ver. I (Nov - Dec 018), PP 6-30 www.osrournals.org Numercal Smulaton of One-Dmensonal Wave Equaton by Non-Polynomal
Math 20C Multivariable Calculus Lecture 5 1. Lines and planes. Equations of lines (Vector, parametric, and symmetric eqs.). Equations of lines
Mt 2C Multivrible Clculus Lecture 5 1 Lines nd plnes Slide 1 Equtions of lines (Vector, prmetric, nd symmetric eqs.). Equtions of plnes. Distnce from point to plne. Equtions of lines Slide 2 Definition
12 Basic Integration in R
14.102, Mt for Economists Fll 2004 Lecture Notes, 10/14/2004 Tese notes re primrily bsed on tose written by Andrei Bremzen for 14.102 in 2002/3, nd by Mrek Pyci for te MIT Mt Cmp in 2003/4. I ve mde only
Statistics and Probability Theory in Civil, Surveying and Environmental Engineering
Statstcs and Probablty Theory n Cvl, Surveyng and Envronmental Engneerng Pro. Dr. Mchael Havbro Faber ETH Zurch, Swtzerland Contents o Todays Lecture Overvew o Uncertanty Modelng Random Varables - propertes
Degrees of Freedom. Spherical (ball & socket) 3 (3 rotation) Two-Angle (universal) 2 (2 rotation)
ME 6590 Multbody Dynamcs Connectn Jonts Part I o Connectn jonts constran te relatve moton between adjonn bodes n a multbody system. Jonts rane rom allown no relatve moton (a rd jont) to allown all motons
DYNAMIC PROPAGATION OF A WEAK-DISCONTINUOUS INTERFACE CRACK IN FUNCTIONALLY GRADED LAYERS UNDER ANTI-PLANE SHEAR
8 TH INTERNTIONL CONFERENCE ON COMPOSITE MTERILS DYNMIC PROPGTION OF WEK-DISCONTINUOUS INTERFCE CRCK IN FUNCTIONLLY GRDED LYERS UNDER NTI-PLNE SHER J.W. Sn *, Y.S. Lee, S.C. Km, I.H. Hwng 3 Subsystem Deprtment,
CENTROID (AĞIRLIK MERKEZİ )
CENTOD (ĞLK MEKEZİ ) centrod s a geometrcal concept arsng from parallel forces. Tus, onl parallel forces possess a centrod. Centrod s tougt of as te pont were te wole wegt of a pscal od or sstem of partcles
Complex Variables. Chapter 18 Integration in the Complex Plane. March 12, 2013 Lecturer: Shih-Yuan Chen
omplex Varables hapter 8 Integraton n the omplex Plane March, Lecturer: Shh-Yuan hen Except where otherwse noted, content s lcensed under a BY-N-SA. TW Lcense. ontents ontour ntegrals auchy-goursat theorem
A Theoretical Study on the Rank of the Integral Operators for Large- Scale Electrodynamic Analysis
Purdue Unversty Purdue e-pubs ECE Techncl Reports Electrcl nd Computer Engneerng -22-2 A Theoretcl Study on the Rnk of the Integrl Opertors for Lrge- Scle Electrodynmc Anlyss Wenwen Ch Purdue Unversty,
Numerical Solution of Nonlinear Multi-order Fractional Differential Equations by Implementation of the Operational Matrix of Fractional Derivative
Studes n Nonlner Scences (): 5-, ISSN -9 IOSI Publctons, Numercl Soluton of Nonlner Mult-order Frctonl fferentl Equtons by Implementton of the Opertonl Mtr of Frctonl ervtve M.M. Khder eprtment of Mthemtcs,
Shuai Dong. Isaac Newton. Gottfried Leibniz
Computatonal pyscs Sua Dong Isaac Newton Gottred Lebnz Numercal calculus poston dervatve ntegral v velocty dervatve ntegral a acceleraton Numercal calculus Numercal derentaton Numercal ntegraton Roots
An Ising model on 2-D image
School o Coputer Scence Approte Inerence: Loopy Bele Propgton nd vrnts Prolstc Grphcl Models 0-708 Lecture 4, ov 7, 007 Receptor A Knse C Gene G Receptor B Knse D Knse E 3 4 5 TF F 6 Gene H 7 8 Hetunndn
CENTROID (AĞIRLIK MERKEZİ )
CENTOD (ĞLK MEKEZİ ) centrod s a geometrcal concept arsng from parallel forces. Tus, onl parallel forces possess a centrod. Centrod s tougt of as te pont were te wole wegt of a pscal od or sstem of partcles
Many-Body Calculations of the Isotope Shift
Mny-Body Clcultons of the Isotope Shft W. R. Johnson Mrch 11, 1 1 Introducton Atomc energy levels re commonly evluted ssumng tht the nucler mss s nfnte. In ths report, we consder correctons to tomc levels
MSC: Primary 11A15, Secondary 11A07, 11E25 Keywords: Reciprocity law; octic residue; congruence; quartic Jacobi symbol
Act Arth 159013, 1-5 Congruences for [/] mo ZHI-Hong Sun School of Mthemtcl Scences, Hun Norml Unverst, Hun, Jngsu 3001, PR Chn E-ml: zhhongsun@hoocom Homege: htt://wwwhtceucn/xsjl/szh Abstrct Let Z be
A Family of Multivariate Abel Series Distributions. of Order k
Appled Mthemtcl Scences, Vol. 2, 2008, no. 45, 2239-2246 A Fmly of Multvrte Abel Seres Dstrbutons of Order k Rupk Gupt & Kshore K. Ds 2 Fculty of Scence & Technology, The Icf Unversty, Agrtl, Trpur, Ind
Propagation of error for multivariable function
Propagaton o error or multvarable uncton ow consder a multvarable uncton (u, v, w, ). I measurements o u, v, w,. All have uncertant u, v, w,., how wll ths aect the uncertant o the uncton? L tet) o (Equaton
Lecture: Financing Based on Market Values II
Lectre: Fnancng Based on Market Vales II Ltz Krscwtz & Andreas Löler Dsconted Cas Flow, Secton 2.4.4 2.4.5, Otlne 2.4.4 Mles-Ezzell- and Modglan-Mller Mles-Ezzell adjstment Modglan-Mller adjstment 2.4.5
Mathematical Economics MEMF e ME. Filomena Garcia. Topic 2 Calculus
Mathematcal Economcs MEMF e ME Flomena Garca Topc 2 Calculus Mathematcal Economcs - www.seg.utl.pt/~garca/economa_matematca . Unvarate Calculus Calculus Functons : X Y y ( gves or each element X one element
A Gas Dynamics Method Based on the Spectral Deferred Corrections (SDC) Time Integration Technique and the Piecewise Parabolic Method (PPM)
Amercn Journl of Computtonl Mtemtcs 0 303-37 do:0.436/cm.0.4037 Publsed Onlne December 0 (ttp://www.scp.org/ournl/cm) A Gs Dnmcs Metod Bsed on te Spectrl Deferred Correctons (SDC) Tme Integrton Tecnque
Numerical Solution of Fredholm Integral Equations of the Second Kind by using 2-Point Explicit Group Successive Over-Relaxation Iterative Method
ITERATIOAL JOURAL OF APPLIED MATHEMATICS AD IFORMATICS Volume 9, 5 umercl Soluton of Fredholm Integrl Equtons of the Second Knd by usng -Pont Eplct Group Successve Over-Relton Itertve Method Mohn Sundrm
ACTM State Calculus Competition Saturday April 30, 2011
ACTM State Calculus Competton Saturday Aprl 30, 2011 ACTM State Calculus Competton Sprng 2011 Page 1 Instructons: For questons 1 through 25, mark the best answer choce on the answer sheet provde Afterward
5 The Laplace Equation in a convex polygon
5 Te Laplace Equaton n a convex polygon Te most mportant ellptc PDEs are te Laplace, te modfed Helmoltz and te Helmoltz equatons. Te Laplace equaton s u xx + u yy =. (5.) Te real and magnary parts of an
Research Article On the Upper Bounds of Eigenvalues for a Class of Systems of Ordinary Differential Equations with Higher Order
Hndw Publshng Corporton Interntonl Journl of Dfferentl Equtons Volume 0, Artcle ID 7703, pges do:055/0/7703 Reserch Artcle On the Upper Bounds of Egenvlues for Clss of Systems of Ordnry Dfferentl Equtons
Solubilities and Thermodynamic Properties of SO 2 in Ionic
Solubltes nd Therodync Propertes of SO n Ionc Lquds Men Jn, Yucu Hou, b Weze Wu, *, Shuhng Ren nd Shdong Tn, L Xo, nd Zhgng Le Stte Key Lbortory of Checl Resource Engneerng, Beng Unversty of Checl Technology,
INTRODUCTION TO COMPLEX NUMBERS
INTRODUCTION TO COMPLEX NUMBERS The numers -4, -3, -, -1, 0, 1,, 3, 4 represent the negtve nd postve rel numers termed ntegers. As one frst lerns n mddle school they cn e thought of s unt dstnce spced
DIFFERENTIAL SCHEMES
DIFFERENTIAL SCHEMES RAYMOND T. HOOBLER Dedcated to the memory o Jerry Kovacc 1. schemes All rngs contan Q and are commutatve. We x a d erental rng A throughout ths secton. 1.1. The topologcal space. Let
Integration by Parts for D K
Itertol OPEN ACCESS Jourl Of Moder Egeerg Reserc IJMER Itegrto y Prts for D K Itegrl T K Gr, S Ry 2 Deprtmet of Mtemtcs, Rgutpur College, Rgutpur-72333, Purul, West Begl, Id 2 Deprtmet of Mtemtcs, Ss Bv,
Chapter Simpson s 1/3 Rule of Integration. ( x)
Cpter 7. Smpso s / Rule o Itegrto Ater redg ts pter, you sould e le to. derve te ormul or Smpso s / rule o tegrto,. use Smpso s / rule t to solve tegrls,. develop te ormul or multple-segmet Smpso s / rule
The finite element method explicit scheme for a solution of one problem of surface and ground water combined movement
IOP Conference Seres: Materals Scence and Engneerng PAPER OPEN ACCESS e fnte element metod explct sceme for a soluton of one problem of surface and ground water combned movement o cte ts artcle: L L Glazyrna