Extension of Cubic B-Spline for Solving the Time-Fractional Allen–Cahn Equation in the Context of Mathematical Physics

Abstract

A B-spline is defined by the degree and quantity of knots, and it is observed to provide a higher level of flexibility in curve and surface layout. The extended cubic B-spline (ExCBS) functions with new approximation for second derivative and finite difference technique are incorporated in this study to solve the time-fractional Allen–Cahn equation (TFACE). Initially, Caputo’s formula is used to discretize the time-fractional derivative, while a new ExCBS is used for the spatial derivative’s discretization. Convergence analysis is carried out and the stability of the proposed method is also analyzed. The scheme’s applicability and feasibility are demonstrated through numerical analysis.

On Multiple-Type Wave Solutions for the Nonlinear Coupled Time-Fractional Schrödinger Model

“…They are essential for understanding and predicting the behavior of complex systems in both natural and engineered environments. However, due to the inherent complexity of NLPDEs [1][2][3][4][5][6], finding exact solutions using a single technique is often challenging. To address this, several reliable methods have been proposed, for instance, the modified exp(−ϕ(ω))expansion function [7,8], the sin-Gordon-expansion [9], the G ′ G 2 -expansion function [10], the first integral approach [11], and the Hirota bilinear approach [12,13].…”