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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:
35R30Inverse problems for PDE
35K05Heat equation
65M32Inverse problems (IVP of PDE, numerical methods)
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