Fourth order Douglas implicit scheme for solving three dimension reaction diffusion equation with non-linear source term

This research paper represents a numerical approximation to non-linear three dimension reaction diffusion equation with non-linear source term from population genetics. Since various initial and boundary value problems exist in three dimension reaction diffusion phenomena, which are studied numerica...

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Bibliographic Details
Published in:AIP advances 2017-07, Vol.7 (7), p.075011-075011-11
Main Authors: Hasnain, Shahid, Saqib, Muhammad, Mashat, Daoud Suleiman
Format: Article
Language:English
Subjects:
Alternating direction implicit methods
Boundary value problems
Diffusion
Finite difference method
Norms
Numerical methods
Reaction-diffusion equations
Scientific papers
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Summary:This research paper represents a numerical approximation to non-linear three dimension reaction diffusion equation with non-linear source term from population genetics. Since various initial and boundary value problems exist in three dimension reaction diffusion phenomena, which are studied numerically by different numerical methods, here we use finite difference schemes (Alternating Direction Implicit and Fourth Order Douglas Implicit) to approximate the solution. Accuracy is studied in term of L 2, L ∞ and relative error norms by random selected grids along time levels for comparison with analytical results. The test example demonstrates the accuracy, efficiency and versatility of the proposed schemes. Numerical results showed that Fourth Order Douglas Implicit scheme is very efficient and reliable for solving 3-D non-linear reaction diffusion equation.
ISSN:2158-3226
2158-3226
DOI:10.1063/1.4986322