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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:
65M32Inverse problems (IVP of PDE, numerical methods)
65M06Finite difference methods (IVP of PDE)
65M12Stability and convergence of numerical methods (IVP of PDE)
35K20Second order parabolic equations, initial boundary value problems
35R30Inverse problems for PDE
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