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Numerical solution of fractional diffusion-wave equation based on fractional multistep method

Authors
Journal
Applied Mathematical Modelling
0307-904X
Publisher
Elsevier
Publication Date
Volume
38
Issue
14
Identifiers
DOI: 10.1016/j.apm.2013.11.069
Keywords
  • Fractional Multistep Method
  • Fractional Diffusion-Wave Equation
  • Integro-Differential Equation
  • Central Difference Scheme
Disciplines
  • Computer Science
  • Mathematics

Abstract

Abstract This paper is devoted to application of fractional multistep method in the numerical solution of fractional diffusion-wave equation. By transforming the diffusion-wave equation into an equivalent integro-differential equation and applying Lubich’s fractional multistep method of second order we obtain a scheme of order O(τα+h2) for 1⩽α⩽1.71832 where α is the order of temporal derivative and τ and h denote temporal and spatial stepsizes. The solvability, convergence and stability properties of the algorithm are investigated and numerical experiment is carried out to verify the feasibility of the scheme.

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