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

Saad Z Rida; Anas A M Arafa; Hussein S Hussein; Ismail G Ameen; Marwa M M Mostafa

doi:10.1038/s41598-024-58493-x

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

Sci Rep. 2024 Apr 15;14(1):8683. doi: 10.1038/s41598-024-58493-x.

Authors

Saad Z Rida¹, Anas A M Arafa^{2

3}, Hussein S Hussein¹, Ismail G Ameen¹, Marwa M M Mostafa⁴

Affiliations

¹ Department of Mathematics, Faculty of Science, South Valley University, Qena, 83523, Egypt.
² Department of Mathematics, College of Science, Qassim University, Buraydah, Saudi Arabia.
³ Department of Mathematics and Computer Science, Faculty of Science, Port Said University, Port Said, Egypt.
⁴ Department of Mathematics, Faculty of Science, South Valley University, Qena, 83523, Egypt. marwa.masoud@sci.svu.edu.eg.

PMID: 38622192
DOI: 10.1038/s41598-024-58493-x

Abstract

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.

Keywords: Fractional derivatives; Hyperbolic equation with time fractional; Numerical results.; Residual power series algorithm; Shifted Chebyshev polynomials of the second kind; Time fractional pseudo hyperbolic equations.