Numerical Analysis of Fisher Equation

The Fisher Equation had been solved numerically by using two Methods of Finite Differences Methods. The First is Explicit Scheme Method and the Second is CrankNicholson Method. A Comparison had been made between these two methods and we find that the CrankNicholson Method converges towards saturation state u=1 faster than the Explicit Scheme Method (Table 1). Also the numerical stability for both Methods had been made, the Explicit Scheme Method is conditionally stable and the condition is , while CrankNicholson Method has the condition for step size, but time step is unconditionally stable.