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.


65M32 Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs
65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35R30 Inverse problems for PDEs
35K15 Initial value problems for second-order parabolic equations
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