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An adaptive difference scheme for nonstationary one-dimensional problems. (Russian. English summary) Zbl 0753.65076

Authors’ summary: An attempt of theoretically formulating an adaptive problem based on a variational method is made, i.e. some minimization problem with concrete control parameters is formulated. An adaptive difference algorithm based on a predictor-corrector technique and on reinterpolating solutions on different grids is formulated, stability and convergence of the algorithm are investigated and computational results are presented.

MSC:

65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
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