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Balancing space and time errors in the method of lines for parabolic equations. (English) Zbl 0725.65087
Strategies for selecting error tolerances are discussed for the solution of parabolic partial differential equations by methods in which a package for ordinary differential equations in time is combined with some spatial discretization. The aim of the proposed method is to ensure that the global error is due principally to the spatial discretization.

MSC:
65M20 Method of lines for initial value and initial-boundary value problems involving PDEs
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
35K15 Initial value problems for second-order parabolic equations
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