چكيده به لاتين
Modelling of many phenomena in physics and engineering are lead to integral equations with the weakly singular kernel. In recent years, the extensive use of these equations has caused many researchers have focused on providing appropriate methods for the numerical solution of them. For this purpose, the main objective of this thesis is to solve integral equations with the weakly singular kernel particularly in the nonlinear case using the projection methods. To achieve this goal, due to abundant strength points of the Sinc approximation with the single exponential (SE) and double exponential (DE) transformations, they are used. Also, among the projection methods, collocation method is applied to convert the weakly singular integral equations to the
nonlinear algebraic system. It is worth noting for solving system of nonlinear equations, Newton's method is used. Based on error analysis, have been shown that the proposed methods have exponential convergence. In each chapter, the accuracy and efficiency of the proposed methods have been tested with a number of numerical examples. The numerical results indicate that compared with other methods, the proposed methods are more accurate.