Spectral shifted Chebyshev collocation technique with residual power series algorithm for time fractional problems

• Published in: Scientific reports Vol. 14; no. 1; pp. 8683 - 14
• Main Authors: Rida, Saad. Z., Arafa, Anas. A. M., Hussein, Hussein. S., Ameen, Ismail G., Mostafa, Marwa. M. M.
• Format: Journal Article
• Language: English
• Published: London Nature Publishing Group UK 15.04.2024; Nature Publishing Group; Nature Portfolio
• Subjects: 639/705; 639/705/1045; Algorithms; Approximation; Differential equations; Error analysis; Fractional derivatives; Humanities and Social Sciences; Hyperbolic equation with time fractional; Mathematics; multidisciplinary; Numerical results; Ordinary differential equations; Partial differential equations; Physics; Power; Residual power series algorithm; Science; Science (multidisciplinary); Shifted Chebyshev polynomials of the second kind; Time fractional pseudo hyperbolic equations; Time fractional pseudo hyperbolic equations; Shifted Chebyshev polynomials of the second kind; Residual power series algorithm; Fractional derivatives; Hyperbolic equation with time fractional; Numerical results
• ISSN: 2045-2322; 2045-2322
• DOI: 10.1038/s41598-024-58493-x

In this paper, two problems involving nonlinear time fractional hyperbolic partial differential equations (PDEs) and time fractional pseudo hyperbolic PDEs with nonlocal conditions are presented. Collocation technique for shifted Chebyshev of the second kind with residual power series algorithm (CTSCSK-RPSA) is the main method for solving these problems. Moreover, error analysis theory is provided in detail. Numerical solutions provided using CTSCSK-RPSA are compared with existing techniques in literature. CTSCSK-RPSA is accurate, simple and convenient method for obtaining solutions of linear and nonlinear physical and engineering problems.