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A method based on Legendre Pseudo-Spectral Approximations for Solving Inverse Problems of Parabolic Types Equations |
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PP: 81-90 |
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Author(s) |
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M. A. Abdelkawy,
Engy A. Ahmed,
P. Sanchez,
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Abstract |
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| 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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