Gegenbauer wavelets collocation technique for the nonlinear Fisher’s reaction–diffusion equation with application arising in biological and chemical sciences

This paper studies the nonlinear Fisher’s equation, a second-order parabolic partial differential equation, and the wavelets collocation method for solving it. The Gegenbauer wavelets collocation technique (GWCT) is used to solve the nonlinear Fisher’s equation. Using the Gegenbauer wavelets, we created the operational matrices of integration. Nonlinear Fisher’s equation is transformed into a system of algebraic equations using the characteristics of the Gegenbauer wavelets expansions and the operational matrix of integration, which speeds up processing. This system of algebraic equations is solved by the Newton-iterative technique to find the unknown coefficients and to obtain the approximate solution for this equation. We present numerical examples to show the efficacy and precision of the approach. The numerical results imply that the projected approach is reasonably close to the exact solution compared with the existing solutions available in the literature. These results show that the projected scheme is computingly simple, reliable, and resilient.