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Abstract A Legendre-Galerkin Chebyshev collocation method is presented for the parabolic inverse problem with control parameters. Optimal order of convergence of the semi-discrete method is obtained in L 2 -norm… Click to show full abstract
Abstract A Legendre-Galerkin Chebyshev collocation method is presented for the parabolic inverse problem with control parameters. Optimal order of convergence of the semi-discrete method is obtained in L 2 -norm for the nonlinear term being not globally Lipschitz continuous. For time-discretization, a Legendre-tau method is applied. The method is implemented by the explicit-implicit iterative method. Suitable basis functions are constructed leading to sparse matrices, and the nonlinear term is collocated at the Chebyshev-Gauss-Lobatto points computed explicitly by the fast Legendre transform. Numerical results are given to show the efficiency and capability of this space-time spectral method.
Journal Title: Applied Numerical Mathematics
Year Published: 2021
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