A new numerical scheme non-polynomial spline for solving generalized time fractional Fisher equation

Abstract

In this paper, a novel numerical scheme is developed using a new construct by non-polynomial spline for solving the time fractional Generalize Fisher equation. The proposed models represent bacteria, epidemics, Brownian motion, kinetics of chemicals and fuzzy systems. The basic concept of the new approach is constructing a non-polynomial spline with different non-polynomial trigonometric and exponential functions to solve fractional differential equations. The investigated method is demonstrated theoretically to be unconditionally stable. Furthermore, the truncation error is analyzed to determine the or-der of convergence of the proposed technique. The presented method was tested in some examples and compared graphically with analytical solutions for showing the applicability and effectiveness of the developed numerical scheme. In addition, the present method is compared by norm error with the cubic B-spline method to validate the efficiency and accuracy of the presented algorithm. The outcome of the study reveals that the developed construct is suitable and reliable for solving nonlinear fractional differential equations.