Operational matrices with respect to Hermite polynomials and their applications in solving linear differential equations with variable coefficients

Subject Areas : Linear and multilinear algebra; matrix theory

Z. Kalateh Bojdi ¹ , S. Ahmadi-Asl ² , A. Aminataei ³

1 - Department of Mathematics, Birjand University, Birjand, Iran
2 - Department of Mathematics, Birjand University, Birjand, Iran
3 - Faculty of Mathematics, K. N. Toosi University of Technology, P.O. Box 16315-1618, Tehran, Iran

Received: 2013-01-01 Accepted : 2013-01-01 Published : 2013-06-01

Keywords: Operational matrices, Hermite polynomials, Linear differential equations with variable coefficients,

Abstract :

In this paper, a new and efficient approach is applied for numerical approximationof the linear differential equations with variable coeffcients based on operational matriceswith respect to Hermite polynomials. Explicit formulae which express the Hermite expansioncoeffcients for the moments of derivatives of any differentiable function in terms of theoriginal expansion coefficients of the function itself are given in the matrix form. The mainimportance of this scheme is that using this approach reduces solving the linear differentialequations 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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