Inicio  /  Computation  /  Vol: 12 Par: 3 (2024)  /  Artículo
ARTÍCULO
TITULO

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

Mubeen Fatima    
Ravi P. Agarwal    
Muhammad Abbas    
Pshtiwan Othman Mohammed    
Madiha Shafiq and Nejmeddine Chorfi    

Resumen

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.

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