Numerical Solution of Diffusion and Reaction-Diffusion Partial Integro-Differential Equations

In this paper, a collocation method based on Haar wavelet is developed for numerical solution of diffusion and reaction-diffusion partial integro-differential equations. The equations are parabolic partial integro-differential equations and we consider both one-dimensional and two-dimensional cases. Such equations have applications in several practical problems including population dynamics. An important advantage of the proposed method is that it can be applied to both linear as well as nonlinear problems with slide modification. The proposed numerical method is validated by applying it to various benchmark problems from the existing literature. The numerical results confirm the accuracy, efficiency and robustness of the proposed method.