Document Details

Document Type : Thesis 
Document Title :
On some numerical treatments of volterra Fred holm integrad equations.
بعض المعالجات العددية لمعادلات فولتيرا – فردهولم التكاملية.
 
Subject : Sciences Faculty for Girls 
Document Language : Arabic 
Abstract : The theory application of integral equations, with its different kinds and kernels, is an important subject within applied sciences. Integral equations are used as mathematical models for many and varied physical situations. Also, the rapid development of computer engineering has aroused the considerable interest of researchers for the development of universal numerical methods for the solution of applied problems. Many different methods can be used for solving the integral equation analytically. In this thesis we study Volterra-Fredholm integral equation and mixed integral equation in the space either it's linear or nonlinear if the kernel with respect to time and the kernel with respect to position are continuous or singular. We choose some kinds of singular kernels as: Carleman kernel, Caushy kernel, Hilbert kernel and logarithmic kernel. And we solve our problem using the most two famous numerical methods Toeplitz matrix method and Product Nystrom method. Also we used another numerical methods if the kernel is continuous for the time and position which are: Collocation method and Galerkin method. We study the existence of a unique solution at each problem when it's in the previous space or when it moves to another one. Numerical results are introduced and error is computed in each case using some programs and we conclude by the relationship between the error and the other factors which are: time, dividing the interval , Possion ratio and Lamy coefficient. 
Supervisor : DR. FATHEAH AL HENDI 
Thesis Type : Doctorate Thesis 
Publishing Year : 1431 AH
2010 AD 
Added Date : Tuesday, June 1, 2010 

Researchers

Researcher Name (Arabic)Researcher Name (English)Researcher TypeDr GradeEmail
خديجة محمد أبو النجاAbu Alnaja, Khadijah MohammedResearcherDoctorate 

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