Numerical simulations of 2D fractional subdiffusion problems

Hermann BRUNNER, Leevan LING*, Masahiro Yamamoto

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

91 Citations (Scopus)

Abstract

The growing number of applications of fractional derivatives in various fields of science and engineering indicates that there is a significant demand for better mathematical algorithms for models with real objects and processes. Currently, most algorithms are designed for 1D problems due to the memory effect in fractional derivatives. In this work, the 2D fractional subdiffusion problems are solved by an algorithm that couples an adaptive time stepping and adaptive spatial basis selection approach. The proposed algorithm is also used to simulate a subdiffusion-convection equation.

Original languageEnglish
Pages (from-to)6613-6622
Number of pages10
JournalJournal of Computational Physics
Volume229
Issue number18
DOIs
Publication statusPublished - Sep 2010

Scopus Subject Areas

  • Numerical Analysis
  • Modelling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

  • Adaptive greedy algorithm
  • Collocation
  • Fractional differential equations
  • Geometric time grids
  • Kansa's method
  • Radial basis functions

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