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Turkish Journal of Mathematics

DOI

10.55730/1300-0098.3323

Abstract

The main interest of this paper is to propose a numerical scheme in order to solve linear systems of Volterra-Fredholm integro-differential equations given with mixed conditions. The proposed method is a weighted residual scheme which uses monomials up to a prescribed degree $N$ as the basis functions. By taking inner product of the equation system with the elements of this basis set in a Galerkin-like fashion, the original problem is transformed into a linear algebraic equation system. After a suitable incorporation of the mixed conditions, a final algebraic system is obtained, from which the approximate solutions of the problem are computed. The proposed numerical scheme is illustrated with example problems taken from the literature.

Keywords

Volterra-Fredholm integro-differential equations, systems of linear integro-differential equations, method of weighted residuals, Galerkin method, method of moments, numerical solutions

First Page

3121

Last Page

3138

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