Exponential B-splines Galerkin Method for the Numerical Solution of the Fisher's Equation

A finite element solution of the Fisher's equation based on the Galerkin method whose weight and shape functions are exponential B-splines are constructed. A travelling wave propagation having analytical solution is studied to compare results in term of the maximum error norm. Both steep and flat initial disturbances are shown to see effects of the diffusion and reaction, form two progressive waves propagating in both opposite directions at long run of the algorithm. The shape and the speed of the long term progressive waves are observed not to depend on the initial disturbance. Graphical solutions and tabulated values are presented to show efficiency of the method.