NUMERICAL APPROXIMATION OF TIME-FRACTIONAL KLEIN–GORDON EQUATION USING B-SPLINE COLLOCATION TECHNIQUES

Javeria Kousar; Muhammad Amin; Manzar 	 Abbas; Ayesha Samra

doi:10.71146/kjmr590

Authors

Javeria Kousar Faculty of Sciences, The Superior University, Lahore, Pakistan Author
Muhammad Amin Faculty of Sciences, The Superior University, Lahore, Pakistan Author
Manzar Abbas Faculty of Sciences, The Superior University, Lahore, Pakistan Author
Ayesha Samra Faculty of Sciences, The Superior University, Lahore, Pakistan Author

DOI:

https://doi.org/10.71146/kjmr590

Keywords:

Time-fractional Klein-Gordon equation, Caputo derivative, Hybrid cubic B-Spline, Finite difference method, Fractional differential equations, Collocation technique

Abstract

This study proposes a numerical technique based on a hybrid cubic B-Spline function for obtaining approximate solutions to the time-fractional Klein-Gordon equation. Fractional derivative is discretized using a finite difference approach in Caputo sense, while the spatial domain is handled through the application of a hybrid cubic B-Spline scheme on a structured grid. To assess the accuracy and performance of the method, some computational experiments have been conducted. The outcomes demonstrate that the proposed technique delivers superior accuracy and computational efficiency when compared to several existing schemes in the literature.