A Chebyshev collocation method for nonlinear fractional Fisher s equation

The fractional Fisher s equation can be used for anomalous population, such as ananomalous population of human, trees, cells or neutrons in a nuclear reactor. In thispaper, we use collocation method based on Chebyshev polynomials to solve nonlinearfractional Fisher s equation. To this end, we obtain a system of nonlinear equationswhich can be solved by Newton s method. Numerical examples show the e ciency ande ectiveness of the method. Like other spectral methods we observe that the approxima-tion is exact for solutions of polynomial types.

Keywords:

Chebyshev collocation method , Nonlinear fractional partial di erentialequations , Di usion equation , Fisher s equation