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A numerical method for backward parabolic problems with non-selfadjoint elliptic operators. (English) Zbl 0976.65080
A method for the solution of backward parabolic problems with non-selfadjoint elliptic operators is presented. The method employs a quasi-solution approach and is based on the separation of the problem into a sequence of well-posed forward problems on the entire mesh and an ill-posed system of algebraic equations on a coarser submesh. A stability result for the forward problem is obtained. Using this result, the existence of a quasi-solution of the backward problem is proved.

MSC:
65M06Finite difference methods (IVP of PDE)
65M12Stability and convergence of numerical methods (IVP of PDE)
35K15Second order parabolic equations, initial value problems
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References:
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