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

Journal of Linear and Topological Algebra

مقاله 5، دوره 02، شماره 02، شهریور 2013، صفحه 91-103   

نوع مقاله: Research Paper

نویسندگان

Z. Kalateh Bojdi¹؛ S. Ahmadi-Asl¹؛ A. Aminataei²

¹Department of Mathematics, Birjand University, Birjand, Iran

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

چکیده

In this paper, a new and efficient approach is applied for numerical approximation of the linear differential equations with variable coeffcients based on operational matrices with respect to Hermite polynomials. Explicit formulae which express the Hermite expansion coeffcients for the moments of derivatives of any differentiable function in terms of the original expansion coefficients 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 differential 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.

کلیدواژه‌ها

Operational matrices؛ Hermite polynomials؛ Linear differential equations with variable coefficients

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