Advanced Methods for Conformable Time-Fractional Differential Equations: Logarithmic Non-Polynomial Splines

Abstract

In this study, we present a numerical method named the logarithmic non-polynomial spline method. This method combines conformable derivative, finite difference, and non-polynomial spline techniques to solve the nonlinear inhomogeneous time-fractional Burgers–Huxley equation. The developed numerical scheme is characterized by a sixth-order convergence and conditional stability. The accuracy of the method is demonstrated with 3D mesh plots, while the effects of time and fractional order are shown in 2D plots. Comparative evaluations with the cubic B-spline collocation method are provided. To illustrate the suitability and effectiveness of the proposed method, two examples are tested, with the results are evaluated using L2 and L∞ norms.

Keywords

• conformable derivative
• natural Logarithmic non-polynomial splines
• time-fractional Burgers–Huxley equation
• stability analysis