A new approach and solution technique to solve time fractional nonlinear reaction-diffusion equations
type: Item
instance of: scholarly article
title: A new approach and solution technique to solve time fractional nonlinear reaction-diffusion equations
zbMATH Open document ID: 1394.65070
DOI: 10.1155/2015/457013
author: Inci Cilingir Sungu
author: Huseyin Demir
published in: Mathematical Problems in Engineering
publication date: 2018-08-27T00:00:00Z
review text: Summary: A new application of the hybrid generalized differential transform and finite difference method is proposed by solving time fractional nonlinear reaction-diffusion equations. This method is a combination of the multi-time-stepping temporal generalized differential transform and the spatial finite difference methods. The procedure first converts the time-evolutionary equations into Poisson equations which are then solved using the central difference method. The temporal differential transform method as used in the paper takes care of stability and the finite difference method on the resulting equation results in a system of diagonally dominant linear algebraic equations. The Gauss-Seidel iterative procedure then used to solve the linear system thus has assured convergence. To have optimized convergence rate, numerical experiments were done by using a combination of factors involving multi-time-stepping, spatial step size, and degree of the polynomial fit in time. It is shown that the hybrid technique is reliable, accurate, and easy to apply.
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 35R11
Mathematics Subject Classification ID: 35K57
zbMATH DE Number: 6926393
Wikidata QID: Q59118631
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2015/457013
OpenAlex ID: W1493764732
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description: scientific article; zbMATH DE number 6926393