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A New Approach and Solution Technique to Solve Time Fractional Nonlinear Reaction-Diffusion Equations
Joint Authors
Cilingir Sungu, Inci
Demir, Huseyin
Source
Mathematical Problems in Engineering
Issue
Vol. 2015, Issue 2015 (31 Dec. 2015), pp.1-13, 13 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2015-07-02
Country of Publication
Egypt
No. of Pages
13
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Cilingir Sungu, Inci& Demir, Huseyin. 2015. A New Approach and Solution Technique to Solve Time Fractional Nonlinear Reaction-Diffusion Equations. Mathematical Problems in Engineering،Vol. 2015, no. 2015, pp.1-13.
https://search.emarefa.net/detail/BIM-1073875
Modern Language Association (MLA)
Cilingir Sungu, Inci& Demir, Huseyin. A New Approach and Solution Technique to Solve Time Fractional Nonlinear Reaction-Diffusion Equations. Mathematical Problems in Engineering No. 2015 (2015), pp.1-13.
https://search.emarefa.net/detail/BIM-1073875
American Medical Association (AMA)
Cilingir Sungu, Inci& Demir, Huseyin. A New Approach and Solution Technique to Solve Time Fractional Nonlinear Reaction-Diffusion Equations. Mathematical Problems in Engineering. 2015. Vol. 2015, no. 2015, pp.1-13.
https://search.emarefa.net/detail/BIM-1073875
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1073875