^{1}Department of Mathematics, Birjand University, Birjand, Iran;

^{2}Faculty of Mathematics, K. N. Toosi University of Technology, P.O. Box 16315-1618, Tehran, Iran.

Abstract

In this paper, a new and ecient approach is applied for numerical approximation of the linear dierential equations with variable coecients based on operational matrices with respect to Hermite polynomials. Explicit formulae which express the Hermite expansion coecients for the moments of derivatives of any dierentiable function in terms of the original expansion coecients of the function itself are given in the matrix form. The main importance of this scheme is that using this approach reduces solving the linear dierential equations to solve a system of linear algebraic equations, thus greatly simplifying the problem. In addition, two experiments are given to demonstrate the validity and applicability of the method.

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