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Inverse heat problem of determining time-dependent source parameter in reproducing kernel space. (English) Zbl 1256.35206

Summary: A new method by the reproducing kernel Hilbert space is applied to an inverse heat problem of determining a time-dependent source parameter. The problem is reduced to a system of linear equations. The exact and approximate solutions are both obtained in a reproducing kernel space. The approximate solution and its partial derivatives are proved to converge to the exact solution and its partial derivatives, respectively. The proposed method improves the existing method. Our numerical results show that the method is of high precision.

MSC:

35R30 Inverse problems for PDEs
35K05 Heat equation
65M32 Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs
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