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International Journal of Nonlinear Sciences and Numerical Simulation

Editor-in-Chief: Birnir, Björn

Editorial Board Member: Armbruster, Dieter / Bessaih, Hakima / Chou, Tom / Grauer, Rainer / Marzocchella, Antonio / Rangarajan, Govindan / Trivisa, Konstantina / Weikard, Rudi

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2191-0294
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A Lagrange Regularized Kernel Method for Solving Multi-dimensional Time-Fractional Heat Equations

Edson Pindza
  • Edson Pindza, Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria 002, Republic of South Africa,
  • :
/ Jules Clement Mba
  • Jules Clement Mba, Department of Mathematics and Applied Mathematics, University of Johannesburg, P. O. Box 524, Auckland Park 2006, South Africa
  • :
/ Eben Maré
  • Eben Maré, Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria 002, Republic of South Africa
  • :
/ Désirée Moubandjo
  • Désirée Moubandjo, Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria 002, Republic of South Africa,
  • :
Published Online: 2016-12-17 | DOI: https://doi.org/10.1515/ijnsns-2016-0089

Abstract:

Evolution equations containing fractional derivatives can provide suitable mathematical models for describing important physical phenomena. In this paper, we propose an accurate method for numerical solutions of multi-dimensional time-fractional heat equations. The proposed method is based on a fractional exponential integrator scheme in time and the Lagrange regularized kernel method in space. Numerical experiments show the effectiveness of the proposed approach.

Keywords: local spectral methods; Lagrange regularized kernel; time-fractional diffusion equations; exponential integrators

MSC 2010: 337K10; 44A15; 45K05; 65M12; 65M70


Received: 2016-06-14

Accepted: 2016-10-31

Published Online: 2016-12-17

Published in Print: 2017-02-01


Citation Information: International Journal of Nonlinear Sciences and Numerical Simulation. Volume 18, Issue 1, Pages 93–102, ISSN (Online) 2191-0294, ISSN (Print) 1565-1339, DOI: https://doi.org/10.1515/ijnsns-2016-0089, December 2016

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