By Jens Lang

these days there's an expanding emphasis on all points of adaptively gener­ ating a grid that evolves with the answer of a PDE. one other problem is to strengthen effective higher-order one-step integration equipment which could 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 tools of Rosenbrock-type is gifted. it truly is my goal to impart the wonder and complexity present in the theoretical research of the adaptive set of rules proposed right here, in its recognition and in fixing non-trivial complicated difficulties. i'm hoping that this system will locate many extra fascinating functions. Berlin-Dahlem, may well 2000 Jens Lang Acknowledgements i've got regarded ahead to scripting this part because it is a excitement for me to thank all pals who made this paintings attainable and supplied worthwhile 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 perfect views, and from his non-stop motivate­ ment and aid over numerous years. He definitely will forgive me using Rosenbrock equipment instead of extrapolation ways to combine in time.

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