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On the determination of the right-hand side in a parabolic equation. (English) Zbl 1259.65139

An overdetermined initial boundary value problem of parabolic type is analyzed. The parabolic equation has an unknown right hand side; Dirichlet boundary conditions are considered. In this study, difference schemes of first and second order of accuracy are used for the approximate solution of the previously described problem. Stability estimates for the solution of these schemes are established. Since the values of the constants involved in the stability inequalities may be large, the numerical algorithms are tested on an example.

MSC:

65M32 Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35K20 Initial-boundary value problems for second-order parabolic equations
35R30 Inverse problems for PDEs
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