A direct numerical method for approximate solution of inverse reaction diffusion equation via two-dimensional Legendre hybrid functions. (English) Zbl 1442.65228
Summary: In this paper, we propose an efficient numerical method based on two-dimensional hybrid of block-pulse functions and Legendre polynomials for numerically solving an inverse reaction diffusion equation. The main idea of the present method is based upon some of the important benefits of the hybrid functions such as high accuracy, wide applicability, and adjustability of the orders of the block-pulse functions and Legendre polynomials to achieve highly accurate numerical solutions. By using the spectral method, inverse reaction diffusion equation with initial and boundary conditions would reduce to a system of nonlinear algebraic equations. Due to the ill-posed system of nonlinear algebraic equations, a regularization scheme is employed to obtain a numerical stable solution. Finally, some numerical examples are presented to show the accuracy and effectiveness of this method.
MSC:
| 65M32 | Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs |
| 65M30 | Numerical methods for ill-posed problems for initial value and initial-boundary value problems involving PDEs |
| 65M70 | Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs |
| 65H10 | Numerical computation of solutions to systems of equations |
| 65F22 | Ill-posedness and regularization problems in numerical linear algebra |
| 35K57 | Reaction-diffusion equations |
Keywords:
reaction diffusion equation; hybrid of block-pulse functions and Legendre polynomials; spectral methods; inverse problems; ill-posed problems; regularizationReferences:
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