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

Shahid Hasnain | Zendy; Muhammad Saqib | Zendy; Daoud S. Mashat | Zendy

Open Access

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

Author(s) -

Shahid Hasnain,

Muhammad Saqib,

Daoud S. Mashat

Publication year - 2017

Publication title -

aip advances

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.421

H-Index - 58

ISSN - 2158-3226

DOI - 10.1063/1.4986322

Subject(s) - dimension (graph theory) , term (time) , mathematics , reaction–diffusion system , diffusion equation , diffusion , population , finite difference method , boundary value problem , approximation error , numerical analysis , finite difference , mathematical analysis , physics , demography , economy , quantum mechanics , sociology , pure mathematics , economics , thermodynamics , service (business)

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 L2, 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

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