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A tau method for the one-dimensional parabolic inverse problem subject to temperature overspecification. (English) Zbl 1125.65340
Summary: An approximational technique based on shifted Legendre-tau ideas is presented for the one-dimensional parabolic inverse problem with a control parameter. The method consists of expanding the required approximate solution as the elements of a shifted Legendre polynomial. Using the operational matrices we reduce the problem to a set of algebraic equations. A numerical example is included to demonstrate the validity and applicability of the technique and a comparison is made with existing results. The method is easy to implement and produces very accurate results.

MSC:
65M32Inverse problems (IVP of PDE, numerical methods)
65M70Spectral, collocation and related methods (IVP of PDE)
35R30Inverse problems for PDE
35K15Second order parabolic equations, initial value problems
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References:
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