By Jens Lang

these days there's an expanding emphasis on all facets of adaptively gener­ ating a grid that evolves with the answer of a PDE. one other problem is to enhance effective higher-order one-step integration equipment which may deal with very stiff equations and which permit us to house a spatial grid in at any time when step with none particular problems. during this monograph a mix of either error-controlled grid refinement and one-step equipment of Rosenbrock-type is gifted. it's my purpose to impart the sweetness and complexity present in the theoretical research of the adaptive set of rules proposed the following, in its attention and in fixing non-trivial advanced difficulties. i am hoping that this technique will locate many extra fascinating purposes. Berlin-Dahlem, may possibly 2000 Jens Lang Acknowledgements i've got seemed ahead to scripting this part because it is a excitement for me to thank all associates who made this paintings attainable and supplied beneficial enter. i need to precise my gratitude to Peter Deuflhard for giving me the oppor­ tunity to paintings within the box of clinical Computing. i've got benefited immensly from his support to get the suitable views, and from his non-stop inspire­ ment and aid over a number of years. He definitely will forgive me using Rosenbrock equipment instead of extrapolation the right way to combine in time.

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