Numerical solutions of the nonlinear Fisher’s equation using a one-level meshless method

This study introduces a relatively new numerical technique for solving one-dimensional Fisher’s equation. The proposed numerical technique is a simple direct meshless method, which is based on the collocation scheme. To circumvent the traditional two-level numerical procedure, the space-time radial basis function is considered. Under such circumstances, the time-dependent one-dimensional nonlinear Fisher’s equation can be solved by a one-level numerical procedure. Several numerical results are investigated to show advantages of the proposed meshless method.