Abstract
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.
Highlights
Reaction diffusion equations arise as the models for the densities of substances or organisms which disperse through space by Brownian motion, random walks, hydrodynamic turbulence, or similar mechanisms, and that react with each other and their surroundings in ways that affect their local densities.[1]
There are three major types of ecological phenomena that are supported by reaction diffusion equations: the existence of a minimal patch size necessary to support a population, the presence of travelling wave fronts corresponding to biological invasions, and the formation of spatial patterns.[1,2,3,4]
Figures (1, 2, 3) show results for Alternating Direction Implicit (ADI) scheme at time t = 1 at three different grid sizes as we mentioned in figures
Summary
Reaction diffusion equations arise as the models for the densities of substances or organisms which disperse through space by Brownian motion, random walks, hydrodynamic turbulence, or similar mechanisms, and that react with each other and their surroundings in ways that affect their local densities.[1].
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
