A Hermite Collocation Method for the Approximate Solutions of High-Order Linear Fredholm Integro-Differential Equations

In this study, a Hermite matrix method is presented to solve high-order linear Fredholm integro-differential equations with variable coefficients under the mixed conditions in terms of the Hermite polynomials. The proposed method converts the equation and its conditions to matrix equations, which correspond to a system of linear algebraic equations with unknown Hermite coefficients, by means of collocation points on a finite interval. Then, by solving the matrix equation, the Hermite coefficients and the polynomial approach are obtained. Also, examples that illustrate the pertinent features of the method are presented; the accuracy of the solutions and the error analysis are performed. (C) 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 27: 1707-1721, 2011