On the Approximate Solutions For Some Classes of Integral Equations

This thesis is devoted to study the numerical solutions of some classes of integralequations, where we have studied the following:The applicability of Variational iteration method to obtain the numerical solutionof Volterra and Fredholm integral equations of the second kind. The method constructsa convergent sequence of functions, which approximates the exact solution with few iterations.The Homotopy perturbation method has been introduce to obtain the numerical solutionof Volterra and Fredholm integral equations of the second kind and compare theresults with the Variational iteration method.A Chebyshev collocation method has been presented to solve nonlinear Fredholm integralequations in terms of Chebyshev polynomials, we have a matrix equation whichcorresponds to a system of nonlinear algebraic equations with unknown Chebyshev coefficients.The approximate solution of linear and nonlinear generalized Abel integral equationhas been studied by using Adomian decomposition method.An efficient numerical method for the solution of sliding contact problems is proposed.Explicit results for the Chebysheve numerical integration scheme for singular integralequations of the second kind with Cauchy kernels are presented.