Efficient Spectral Collocation Algorithm for Solving Parabolic Inverse Problems
Copyright policy )Efficient Spectral Collocation Algorithm for Solving Parabolic Inverse Problems
This paper reports a new Legendre–Gauss–Lobatto collocation (SL-GL-C) method to solve numerically two partial parabolic inverse problems subject to initial-boundary conditions. The 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 nonclassical parabolic initial-boundary value problems. Accordingly, the inverse problem is reduced into a system of ordinary differential equations (ODEs) and afterwards, such system can be solved numerically using implicit Runge–Kutta (IRK) method of order four. Four examples are introduced to demonstrate the applicability, validity, effectiveness and stable approximations of the present method. Numerical results show the exponential convergence property and error characteristics of presented method.
- Imam Muhammad ibn Saud Islamic University Saudi Arabia
- Beni-Suef University Egypt
- Islamic University Bangladesh
systems of ordinary differential equations, inverse problems, Gauss-Lobatto quadrature, Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs, nonlinear parabolic partial differential equations, pseudo-spectral scheme, Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
systems of ordinary differential equations, inverse problems, Gauss-Lobatto quadrature, Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs, nonlinear parabolic partial differential equations, pseudo-spectral scheme, Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
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