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Stability and convergence at the PDE/stiff ODE interface. (English) Zbl 0671.65078

Many numerical schemes for evolutionary partial differential equations can be viewed as method of lines schemes. The authors’ main purpose is to show the theory of stiff ordinary differential equations (ODEs) to the field of analysis of numerical methods in partial differential equations. In this respect of, important concepts are contractivity one-sided Lipschitz conditions, logarithmic norms, B-convergence and order reduction. They emphasize the relation between the stability and convergence properties of the fully discrete scheme and those of the ODE solver.
Reviewer: M.Z.Qin

MSC:

65M20 Method of lines for initial value and initial-boundary value problems involving PDEs
65L20 Stability and convergence of numerical methods for ordinary differential equations
35G10 Initial value problems for linear higher-order PDEs
35K25 Higher-order parabolic equations
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