Comparative Numerical Study of Spline-Based Numerical Techniques for Time Fractional Cattaneo Equation in the Sense of Caputo–Fabrizio

• Published in: Fractal and fractional 2022-02, Vol.6 (2), p.50
• Main Authors: Yaseen, Muhammad, Nisa Arif, Qamar Un, George, Reny, Khan, Sana
• Format: Article
• Language: English
• Subjects: Approximation; B spline functions; Basis functions; Boundary conditions; Caputo–Fabrizio derivative; Cattaneo equation; Continuity (mathematics); cubic B-splines; Derivatives; extended cubic B-splines; Finite difference method; Linear equations; Mathematical analysis; Ordinary differential equations; Partial differential equations; Stability analysis; trigonometric cubic B-splines
• ISSN: 2504-3110; 2504-3110
• DOI: 10.3390/fractalfract6020050

This study focuses on numerically addressing the time fractional Cattaneo equation involving Caputo–Fabrizio derivative using spline-based numerical techniques. The splines used are the cubic B-splines, trigonometric cubic B-splines and extended cubic B-splines. The space derivative is approximated using B-splines basis functions, Caputo–Fabrizio derivative is discretized, using a finite difference approach. The techniques are also put through a stability analysis to verify that the errors do not pile up. The proposed scheme’s convergence analysis is also explored. The key advantage of the schemes is that the approximation solution is produced as a smooth piecewise continuous function, allowing us to approximate a solution at any place in the domain of interest. A numerical study is performed using various splines, and the outcomes are compared to demonstrate the efficiency of the proposed schemes.