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New algorithms for approximate realization of implicit difference schemes. (English) Zbl 0825.65066
Summary: The present paper treats the construction of estimates for Green’s mesh function of finite difference and finite element operators involved in solving nonstationary heat conduction equations by implicit methods. Using these estimates, a new approach to approximate realization of implicit difference schemes is suggested on the basis of partitioning the spatial mesh domain into small mesh subdomains. Estimates are constructed for the computational cost of realizing implicit schemes with a prescribed accuracy.

MSC:
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
35K05 Heat equation
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