LUCAS POLYNOMIAL SOLUTION FOR NEUTRAL DIFFERENTIAL EQUATIONS WITH PROPORTIONAL DELAYS

S. Gumgum, N. B. Savasaneril, O. K. Kurkcu, M. Sezer

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Abstract

This paper proposes a combined operational matrix approach based on Lucas and Taylor polynomials for the solution of neutral type dierential equations with proportional delays. The advantage of the proposed method is the ease of its application. The method facilitates the solution of the given problem by reducing it to a matrix equation. Illustrative examples are validated by means of absolute errors. Residual error estimation is presented to improve the solutions. Presented in graphs and tables the results are compared with the existing methods in literature.

Keywords

Neutral dierential equations, Lucas and Taylor polynomials, collocation and matrix methods.