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Global error estimation in the method of lines for parabolic equations. (English) Zbl 0659.65081
An algorithmic procedure is proposed fo assessing the error in the numerical solution of partial differential equations (PDE) using the method of lines. It is based on matching existing global error estimating algorithms for initial value problems in ordinary differential equations with estimates for the truncation error associated with the application of the method of lines to the specific PDE under consideration. Numerical experimentation shows that the procedure yields reliable results and therefore merits further research and development.
Reviewer: R.S.Anderssen

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