Application of Some Finite Difference Schemes for Solving One Dimensional Diffusion Equation

Tsegaye Simon, Purnachandra Rao Koya

Abstract


In this paper the numerical solutions of one dimensional diffusion equation using some finite difference methods have been considered. For that purpose three examples of the diffusion equation together with different boundary conditions are examined. The finite difference methods applied on each example are (i) forward time centered space (ii) backward time centered space and (iii) Crank – Nicolson. In each case, we have studied stability of finite difference method and also obtained numerical result. The performance of each scheme is evaluated in accordance with both the accuracy of the solution and programming efforts. The implementation and behavior of the schemes have been compared and the results are illustrated pictorially. It is found in case of the test examples studied here that the Crank – Nicolson scheme gives better approximations than the two other schemes.


Keywords


Crank – Nicolson; Diffusion equation; Forward time centered space; Backward time centered space; Stability.

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