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Recovering a time-dependent coefficient in a parabolic equation from overspecified boundary data using the pseudospectral Legendre method. (English) Zbl 1107.65085
Summary: The aim of this article is to discuss the problem of finding the unknown function $$u(x,t)$$ and the time-dependent coefficient $$a(t)$$ in a parabolic partial differential equation. The pseudospectral Legendre method is employed to solve this problem. The results of numerical experiments are given.

##### MSC:
 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 35K05 Heat equation
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