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.
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