Study on Solution of Non-homogeneous Linear Equation based on Ordinary Differential Equation Driving Jing Zhang
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1 Iteratioal Coeree o Automatio Meaial Cotrol ad Computatioal Egieerig AMCCE 05 Stud o Solutio o No-omogeeous Liear Equatio based o Ordiar Dieretial Equatio Drivig Jig Zag Meaial ad Eletrial Egieerig College Cogqig Teolog ad Busiess istitute Cogqig 4050 Cia jigzag0@ea.et ewords: Ordiar dieretial equatio No-omogeeous liear equatio Two orders Ruge- utta MATLAB Spae solutio. Abstrat. Tis paper itrodues two orders Ruge-utta ordiar dieretial solutio drive i te proess o solvig te o-omogeeous ad uses MATLAB sotware to program te algoritm. Tis paper uses ordiar dieretial solutio metod o M utio to solve o-omogeeous equatio. Troug te alulatio plae ad spae solutio o omogeeous equatio are obtaied iall te arateristi urve is draw. Troug alulatio alulatio speed is ast ad te aura is ig usig MATLAB laguage wi provides a teoretial basis or oomogeeous equatio solutio. Itrodutio Teor o liear dieretial equatios is omplete ad te appliatio sope is ver etesive. Espeiall te two order liear dieretial equatio wit ostat oeiiets it is widel applied i meaial eletrial egieerig et.. Te solutio is geerall troug ivestigatio multipliit o orrespodig arateristi equatio arateristi roots te determie aordig to te o-omogeeous term b usig te metod o udetermied oeiiets or variatio parameters [ ]. Tis paper uses ordiar dieretial equatios to solve o-omogeeous liear equatio ad te solvig proess is as sow i Figure. Ordiar dieretial equatios Two order Ruge-utta No-omogeeous liear equatio MATLAB boudar value solutio MATLAB plae ad spae solutio Fig.: Ordiar dieretial equatio solvig algoritm o o-omogeeous equatio Figure sows te ordiar dieretial equatio solvig algoritm o o-omogeeous equatio [ 4]. From te art it a be see tis paper uses ordiar dieretial drivig metod o two orders Ruge-utta to solve te o-omogeeous equatio ad uses MATLAB sotware to program te algoritm iall boudar value solutio ad te plae spae solutio o oomogeeous dieretial equatio are obtaied. 05. Te autors - Publised b Atlatis Press 80
2 Te Teor Foudatio o No-omogeeous Dieretial Equatio Drive Solutio Te solutio o ostat oeiiet liear dieretial equatio plas a importat role i ordiar dieretial equatios; it is oe o te basi otet o ordiar dieretial equatio sstem wit omplete teor ad ri pratial bagroud espeiall te two order ostat oeiiets liear dieretial equatio is more promiet ous [5-7]. Tis paper disusses te ollowig solvig metod o te two order ostat oeiiet liear dieretial equatio.. Te orrespodig omogeeous liear equatio is: 0. Usig two order Ruge-utta ordiar dieretial equatios drivig metod solves te oomogeeous liear equatio as sow i ormula. µ λ. Were λ ad µ are determied te loal truatio error is: ] [ T µ λ 4 Te oeiiet a be obtaied troug te ormula 5: µ λ. 5 Usig our orders Ruge-utta metod solves te dieretial equatios as sow i te ormula I order to realize te ostat miro deompositio metod o o-omogeeous liear equatio aordig to te above ormulas tis paper uses MATLAB umerial alulatio metod to desig te algoritm. Te program is as ollows: sms ; *- ; a8;b8;- 9;- 9; m80;80;a/ m;b/ ; 8
3 old o or i:m i- *; or j: j- *; deval; / **d; iabs- >/ * / d**/ ; Resear o Ordiar Dieretial Numerial Drive or No-omogeeous Equatio I order to veri te validit ad reliabilit o ordiar dieretial drive umerial solutio or o-omogeeous equatio tis paper uses te ordiar dieretial equatio M utio solutio o MATLABT to solve o-omogeeous equatio ad te alulated te boudar value solutio is as sow i Figure. Fig.: Homogeeous equatio boudar value solutio usig ordiar dieretial equatio drivig As sow i Figure te desriptio o dieretial equatio is ompletel osistet wit te iitial value ad te boudar value is desribed [8]. It will all te bvp5 utio ad te a also be troug te ilie utio or aomous utios diretl. Fig.: No-omogeeous boudar value solutio usig ordiar dieretial equatios drivig As sow i Figure o-omogeeous boudar value solutio is obtaied usig ordiar dieretial equatios drivig [9]. B settig te boudar values te grapi solutio o origial 8
4 equatio is obtaied. No-omogeeous equatio solutio is usig te ordiar dieretial equatio to derease order. Te plae solutio is obtaied as sow i Figure 4. Fig.4: Plae solutio grap Figure 4 sows a arateristi urve o omogeeous equatios. Te urve a use MATLAB visual displa utio to solve as sow i Figure 4 [0]. I te ordiar dieretial equatio drivig metod a smoot urve is obtaied wi is osistet wit te arateristis o oomogeeous equatio. Fig.5: Spae solutio grap I order to mae te solutio o te equatio visualizatio tis paper uses te Plot utio o MATLAB to draw te o-omogeeous liear equatio solutio set as sow i Figure 5 []. Te solutio set is omposed o a series o similar urve ad te sreesot osists wit te D plae setio. Summar Tis paper establises two orders Ruge-utta ordiar dieretial solvig drivig metod o oomogeeous liear equatio ad uses MATLAB sotware to program te algoritm. I order to 8
5 veri te validit ad reliabilit o te ad reliabilit drivig metod tis paper uses te ordiar dieretial equatio solvig M utio o MATLAB to solve o-omogeeous equatio ad te arateristis solutio urve o o-omogeeous liear equatio is obtaied. Troug alulatio te geeral tred o MATLAB umerial solutio is te same as aaltial solutio ad its alulatio speed is aster aura is iger. Reerees [] J. Guo Y. Wu. Appliatio o te superpositio priiple i solutio o ordiar dieretial equatio. Joural o Jiujiag Uiversit NATURAL SCIENCE EDITION 0 : [] F. Yu. Appliatio o separatio metod i solutio o iitial boudar value. Computer CD- ROM sotware ad appliatio 0 7: [] Y.Q. Li S.Y. Xie. Some tougts o te reorm i egieerig uiversit matematis eduatio. Uiversit matematis 04 : 0-0. [4] Y. Wag J.S. Na. Idutive ad dedutive metod i te liear algebra teaig. Higer matematis resear 0 6: [5] X. F. Xu. Matematial modelig tougt ito te eploratio o te liear algebra teaig. Joural o Hubei Poltei Istitute 0 45: [6] P.Y. Ce. Te eploratio ad pratie o teaig reorm o liear algebra ourse. Higer eduatio o siee 0 45: [7] W.X. Ce. Resear about teaig o liear algebra. Higer matematis 0 4: 5-8. [8] J.H. Ce L.B. Li. Aalsis solutio o liear algebrai problems usig utio idea. Uiversit matematial 0 4 5: 5-8. [9] Y.H. La. Te matematis tougt i matematis teaig seepage. Joural o Zogsa Uiversit 0 58: 8-. [0] L. Liu N. Su. Te redued order solutio o N orders ostat oeiiet o-omogeeous liear dieretial equatios. Uiversit mat 0 6: [] D. Zu. Speial solutio ormula o te two order ostat oeiiet o-omogeeous liear dieretial equatios. Higer matematis resear 0 4:
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