Numerical Solution of General Higher-Dimensional Nonlinear Fredholm-Volterra Integral Equations Using Chebyshev Approximation رسالة ماجستير

Abstract

In this work, we study computational methods for solving general one, two and three dimensional nonlinear Fredholm-Volterra Integral Equations of the second kind Using Chebyshev Approximation. The method is based on replacement unknown functions by truncted series of well known Chebyshev expantion function. The final result will be compared with published experimental and theoritical results. Further, in order to find the approximated solution, the Fredholm-Volterra integral Equation of the second kind is converted to a system of non-linear equation using the Chebyshev approximation. Finally, many numerical examples were provided to demonstrate the applicability and the accuracy of the presented method