AN EFFICIENT METHOD FOR A CLASS OF INTEGRO-DIFFERENTIAL EQUATIONS WITH A WEAKLY SINGULAR KERNEL

AN EFFICIENT METHOD FOR A CLASS OF INTEGRO-DIFFERENTIAL EQUATIONS WITH A WEAKLY SINGULAR KERNEL

R. Azimi, R. Pourgholi, A. Tahmasbi

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Abstract

In this work, a class of volterra integro-dierential equation with a weakly singular kernel is discussed. The shifted Legendre Tau method is introduced for nding the unknown function. The proposed method is based on expanding the approximate solution as the elements of a shifted Legendre polynomials. We reduce the problem to a set of algebraic equations by using operational matrices. Also the convergence analysis and error estimation have been discussed and approved with the exact solution. Finally, several numerical examples are given to demonstrate the high accuracy of the method.

Keywords

Shifted Legendre Tau method; Weakly singular kernel; Integro-dierential equation.