Numerical solutions of one-dimensional parabolic convection-diffusion problems arising in biology by the Laguerre collocation method

Burcu G??rb??z, Mehmet Sezer

Abstract


In this work, we present a numerical scheme for the approximate solutions?of the one-dimensional parabolic convection-diffusion model problems.?Diffusion models form a reasonable basis for studying insect and animal?dispersal and invasion, which arise from the question of persistence of endangered?species, biodiversity, disease dynamics, multi-species competition?so on. Convection diffusion problem is also a form of heat and mass transfer?in biological models. The presented method is based on the Laguerre?collocation method used for these problems of differential equations.

In fact, the approximate solution of the problem in the truncated Laguerre?series form is obtained by this method. By substituting truncated?Laguerre series solution into the problem and by using the matrix operations?and the collocation points, the suggested scheme reduces the problem?to a linear algebraic equation system. By solving this equation system, the?unknown Laguerre coecients can be computed. The accuracy and the efficiency of the method is showed by numerical examples and the comparisons?by the other methods.

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DOI: http://dx.doi.org/10.11145/j.biomath.2017.06.047

ISSN 1314-684X (print)
ISSN 1314-7218 (online)