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.
Volterra-Fredholm integro-differential equations, systems of linear integro-differential equations, method of weighted residuals, Galerkin method, method of moments, numerical solutions
KARAÇAYIR, MURAT and YÜZBAŞI, ŞUAYİP
"A Galerkin-type approach to solve systems of linear Volterra-Fredholm integro-differential equations,"
Turkish Journal of Mathematics: Vol. 46:
8, Article 5.
Available at: https://journals.tubitak.gov.tr/math/vol46/iss8/5