Numerical solution of keller-segel equation using finite difference method and method of lines

Abstract

Keller-Segel equation is a nonlinear partial differential equation (PDE) that modelled the movement of cells and organisms in response to chemical attractants, which is known as chemotaxis process. In this study, Keller-Segel (KS) equation is solved numerically by explicit finite difference method (FDM) and method of lines (MOL). The finite difference method is performed forward in time and centered in space meanwhile in the method of lines the solution will incorporate with Euler’s method. Results of numerical experiments are presented and the accuracy of the numerical scheme is investigated by comparing the results with the exact solutions. The computational experiment is conducted using MS Visual C++ and results are presented graphically by MATLAB software. The result from both numerical methods shows good agreement with the exact solutions. From the comparison, both methods are shown to be good numerical approximations as the results obtained show closeness to the exact solution.