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Solution of Density Dependent Nonlinear Reaction-Diffusion Equation Using Differential Quadrature Method
Authors: Gülnihal Meral
Abstract:In this study, the density dependent nonlinear reactiondiffusion equation, which arises in the insect dispersal models, is solved using the combined application of differential quadrature method(DQM) and implicit Euler method. The polynomial based DQM is used to discretize the spatial derivatives of the problem. The resulting time-dependent nonlinear system of ordinary differential equations(ODE-s) is solved by using implicit Euler method. The computations are carried out for a Cauchy problem defined by a onedimensional density dependent nonlinear reaction-diffusion equation which has an exact solution. The DQM solution is found to be in a very good agreement with the exact solution in terms of maximum absolute error. The DQM solution exhibits superior accuracy at large time levels tending to steady-state. Furthermore, using an implicit method in the solution procedure leads to stable solutions and larger time steps could be used.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1071770Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1862
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