RESEARCH ARTICLE
Approximate Petrov–Galerkin Solution for the Time Fractional Diffusion Wave Equation
Ahmed Gamal Atta,
Corresponding Author
Ahmed Gamal Atta
Department of Mathematics, Faculty of Education, Ain Shams University, Cairo, Egypt
Correspondence:
Ahmed Gamal Atta ([email protected])
Contribution: Methodology, Software, Supervision, Writing - original draft, Visualization, Validation, Writing - review & editing, Investigation, Formal analysis, Data curation, Resources, Project administration, Funding acquisition, Conceptualization
Search for more papers by this authorAhmed Gamal Atta,
Corresponding Author
Ahmed Gamal Atta
Department of Mathematics, Faculty of Education, Ain Shams University, Cairo, Egypt
Correspondence:
Ahmed Gamal Atta ([email protected])
Contribution: Methodology, Software, Supervision, Writing - original draft, Visualization, Validation, Writing - review & editing, Investigation, Formal analysis, Data curation, Resources, Project administration, Funding acquisition, Conceptualization
Search for more papers by this authorFirst published: 20 April 2025
Funding: The authors received no specific funding for this work.
ABSTRACT
This paper discusses the Petrov–Galerkin method's application in solving the time fractional diffusion wave equation (TFDWE). The method is based on using two modified sets of shifted fourth-kind Chebyshev polynomials (FKCPs) as basis functions. The explicit forms of all spectral matrices were reported. These forms are essential to transforming the TFDWE and its underlying homogeneous conditions into a matrix system. An appropriate algorithm can be used to solve this system to obtain the desired approximate solutions. The error analysis of the method was studied in depth. Four numerical examples were provided that included comparisons with other existing methods in the literature.
Conflicts of Interest
The authors declare no conflicts of interest.
Open Research
Data Availability Statement
The authors have nothing to report.
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