Ø®Ù„ØªÙ‡ Ø¨Ø¬Ø¯ÛŒ, Ø., Ø§ØÙ…Ø¯ÛŒ Ø§ØµÙ„, Ø., Ø§Ù…ÛŒÙ† Ø¹Ø·Ø§ÛŒÛŒ, Ø. (2013). The Operational matrices with respect to generalized Laguerre polynomials and their applications in solving linear dierential equations with variable coecients. Theory of Approximation and Applications, 9(2), 57-80.

Ø² Ø®Ù„ØªÙ‡ Ø¨Ø¬Ø¯ÛŒ; Ø³ Ø§ØÙ…Ø¯ÛŒ Ø§ØµÙ„; Ø§ Ø§Ù…ÛŒÙ† Ø¹Ø·Ø§ÛŒÛŒ. "The Operational matrices with respect to generalized Laguerre polynomials and their applications in solving linear dierential equations with variable coecients". Theory of Approximation and Applications, 9, 2, 2013, 57-80.

Ø®Ù„ØªÙ‡ Ø¨Ø¬Ø¯ÛŒ, Ø., Ø§ØÙ…Ø¯ÛŒ Ø§ØµÙ„, Ø., Ø§Ù…ÛŒÙ† Ø¹Ø·Ø§ÛŒÛŒ, Ø. (2013). 'The Operational matrices with respect to generalized Laguerre polynomials and their applications in solving linear dierential equations with variable coecients', Theory of Approximation and Applications, 9(2), pp. 57-80.

Ø®Ù„ØªÙ‡ Ø¨Ø¬Ø¯ÛŒ, Ø., Ø§ØÙ…Ø¯ÛŒ Ø§ØµÙ„, Ø., Ø§Ù…ÛŒÙ† Ø¹Ø·Ø§ÛŒÛŒ, Ø. The Operational matrices with respect to generalized Laguerre polynomials and their applications in solving linear dierential equations with variable coecients. Theory of Approximation and Applications, 2013; 9(2): 57-80.

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

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 dierential 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 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 simplify the problem. In addition, several numerical experiments are given to demonstrate the validity and applicability of the method.

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