Comparison of the numerical methods that are used in solving some of the partial differantial equations

In this study, numerical solutions of some partial differential equations are investigated. For this, Burgers and Fisher equations, which we have discussed first, are solved numerically by homotopy perturbation, Adomian decomposition and implicit exponential finite difference methods together with appropriate initial and boundary conditions and compared with the obtained numerical results in a tabular form and shown on the graph. Based on these examples, it has been seen that the implicit exponential finite difference method is more stable than the homotopy perturbation and Adomian decomposition methods. It is well known that Homotopy perturbation and Adomian decomposition methods are also effective methods in solving equations.