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Mathematical Sciences Letters
An International Journal


Volumes > Vol. 4 > No. 1


A method based on Legendre Pseudo-Spectral Approximations for Solving Inverse Problems of Parabolic Types Equations

PP: 81-90
M. A. Abdelkawy, Engy A. Ahmed, P. Sanchez,
This paper reports a new Legendre Gauss-Lobatto collocation (SL-GL-C)method to solve numerically two inverse problems of parabolic partial differential types equations subject to initial-boundary conditions. This problem is reformulated by eliminating the unknown functions using some special assumptions based on Legendre Gauss-Lobatto quadrature rule. The SL-GL-C is utilized to solve non-classical parabolic initial-boundary value problems. Accordingly, the inverse problem is reduced into a system of ordinary differential equations (SODEs) and afterwards, such system can be solved numerically using implicit Runge-Kutta (IRK) method of order four. For demonstrating the robust, effectiveness and stable approximations of the present method, several test examples are presented.

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