A Higher Order Numerical Scheme for Some Nonlinear Differential Equations: Models in Biology

Abstract

In this paper, we develop a numerical scheme based on differential quadrature method to solve nonlinear generalizations of the Fisher and Burgers’ equations with the zero flux on the boundary. In construction of the numerical scheme, quasilinearization is used to tackle the nonlinearity of the problem, which is followed by semi-discretization for spatial direction using differential quadrature method (DQM). Semi-discretization of the problem leads to a system of first order initial value problem. For total discretization, we discretize the system of first order initial value problem resulting from the space semi-discretization using the RK4 scheme with constant step length. The method is analyzed for stability and convergence. Finally, the efficiency of the method is derived via numerical comparison between their numerical solution and the exact solution. L 2 and L ∞ error norms demonstrate the accuracy of the proposed method.