Numerical Solutions of Linear and Nonlinear Fredholm Integro-Differential Equations by Using the Weighted Integral Mean Value Methods

Abstract

In this work, we present a numerical algorithm for approaching the solutions of a specific form of linear and nonlinear Fredholm integro-differential equations. This algorithm is constructed by applying the weighted integral mean value methods, which allow us to convert the proposed equations into a system of algebraic equations, then by solving this system we obtain the approximate solutions. Moreover, we provide some illustrative examples to show the effectiveness and simplicity of the algorithm.

Keywords: Fredholm equations; Integro-differential equations; Degenerate kernels; Weighted integral mean value theorem.

2010 Mathematics Subject Classification. 45B05; 65R20; 26A24