Potential Function in Fredholm Volterra Integral Equation

Transcription

1 Umm Al Qura University Faculty of Applied Sciences Department of Mathematical Sciences Potential Function in Fredholm Volterra Integral Equation A Thesis Submitted in Partial Fulfillment of the Requirements of Master's Degree In Applied Mathematics ( Integral Equations ) Prepared by Researcher Faizah Mohamed Hamdi Al Saedy Supervised by Prof. Mohamed Abdella Ahmed Abdou 1427 AH 2006G ١

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5 جامعة أم القرى (مكة المكرمة) آلية العلوم التطبيقية قسم العلوم الرياضية دالة جهد في معادلة فردهولم فولتيرا التكاملية بحث تكميلي مقدم لنيل درجة الماجستير في الرياضيات التطبيقية ) معادلات تكاملية ( إعداد الباحثة فايزة محمد حمدي الصاعدي تحت إشراف الا ستاذ الدآتور / محمد عبد اللاه أحمد عبده 142٧ ه ٢٠٠٦ م ١٢٦

6 Contents Introduction i v Chapter 1 Basic Concepts 1.1 Definitions and theorems Laplace transformation Classification of integral equations Fredholm theorems for continuous kernel Integral operator Compact operator 28 Chapter 2 Volterra Integral Equation 2.1 Existence and uniqueness solution of Volterra equation The resolvent kernel method Solution method using Laplace transformation Method of successive approximation Volterra integral equation of the first kind 53 Chapter 3 Fredholm Volterra Integral Equation with Potential Kernel 3.1 Introduction Existence and uniqueness solution of the integral equation Continuity and normality of integral operator The kernel of position 75 ٢

7 Chapter 4 Series Method 4.1 Separation of variables method Discussion and special cases 94 Chapter 5 Applications for Potential Kernel 5.1 Electrostatic potential Torsion of an isotropic elastic plate Mechanics and mixed problem Raditions and molecular condition Discussion and results Appendix. 114 References أ ج. summary Arabic ٣