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Haar wavelet method for two-dimensional parabolic inverse problem with a control parameter. (English) Zbl 1466.65107

Summary: In this paper, we present a numerical method based on Haar wavelets for solving multidimensional parabolic inverse problem with a control parameter. In this method, the highest derivative appearing in the parabolic equation is expanded into Haar wavelet series. Taylor series expansion and cubic spline interpolation are used to approximate the control parameter. We have computed Haar matrices and Haar integral matrices only once and used the same for different time iterations which lead to a significant reduction in the computational cost. Numerical experiments are performed on some test problems. It is found that numerical results are in good agreement with the exact solution.

MSC:

65M32 Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs
65T60 Numerical methods for wavelets
65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
65M22 Numerical solution of discretized equations for initial value and initial-boundary value problems involving PDEs
65D07 Numerical computation using splines
35K20 Initial-boundary value problems for second-order parabolic equations
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References:

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