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Journal of Scientific Computing

, Volume 81, Issue 3, pp 1945–1962 | Cite as

Explicit Time Stepping of PDEs with Local Refinement in Space-Time

  • Dylan AbrahamsenEmail author
  • Bengt Fornberg
Article
  • 101 Downloads

Abstract

Traditional numerical time stepping allows variable node densities in space, but not also in time. Having the ability to utilize nodes that are placed irregularly in the space-time domain leads to many advantages when solving time dependent problems. In this paper we introduce a new method utilizing the radial basis function generated finite difference approach in order to accomplish this goal. Benefits include improved stability conditions and the option to use small time steps only in select spatial regions.

Keywords

Radial basis functions PDEs Space-time Meshless MOL 

Mathematics Subject Classification

65M50 65M70 65M06 65M20 

Notes

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Applied MathematicsUniversity of ColoradoBoulderUSA

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