Fibonacci Wavelet Method for the Numerical Solution of Nonlinear Reaction-Diffusion Equations of Fisher-Type

Abstract

This article aims to propose an efficient Fibonacci wavelet-based collocation method for solving the nonlinear reaction-diffusion equation of Fisher-type. The underlying numerical scheme starts by formulating operational matrices of integration corresponding to the Fibonacci wavelets. Besides, we study the error analysis and convergence theorem of the proposed technique. Subsequently, a set of algebraic equations are formed corresponding to the given problem, which could be handled via any conventional method, for instance, the Newton iteration technique. To demonstrate the efficiency of the proposed wavelet-based numerical method, we compare the obtained absolute, L∞, L2, and root mean square (RMS) error norms with the existing Lie symmetry method and cubic trigonometric B-spline (CTB) differential quadrature method in tabular form. From the numerical outcomes, it is ascertained that the proposed numerical technique is computationally more effective and yields precise outcomes in comparison to the existing ones.