The Operational matrices with respect to generalized Laguerre polynomials and their applications in solving linear di erential equations with variable coecients

Document Type: Research Articles


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In this paper, a new and ecient approach based on operational matrices with respect to the gener-
alized Laguerre polynomials for numerical approximation of the linear ordinary di erential equations
(ODEs) with variable coecients is introduced. Explicit formulae which express the generalized La-
guerre expansion coecients for the moments of the derivatives of any di erentiable 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 di erential equations
to solve a system of linear algebraic equations, thus greatly simplify the problem. In addition, several
numerical experiments are given to demonstrate the validity and applicability of the method.

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