Exponentially fitted methods for solving time fractional nonlinear reaction–diffusion equation

W.K. Zahra, M.A. Nasr and M. Van Daele

Applied Mathematics and Computation, 2019, vol. 358, issue C, 468-490

Abstract: In this article, we will develop a new numerical scheme with the second order in time and a class of fourth order or sixth order in space based on the exponential fitting techniques to approximate the nonlinear time fractional reaction–diffusion equation with fixed order and distributed order derivatives. These techniques depend on a parameter, which will be used to annihilate the error and increase the order of accuracy. The proposed methods are proved to be unconditionally stable and convergent by Fourier analysis. Also, the theoretical results and the effectiveness of the numerical scheme are confirmed by numerical test problems and a comparison with other methods is presented.

Keywords: Exponential fitting; Parameter selection; Distributed order time fractional; Time fractional reaction–diffusion equations; Stability analysis; Convergence analysis (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300319303017
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:358:y:2019:i:c:p:468-490

DOI: 10.1016/j.amc.2019.04.019

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().