Work

A Refined Spectral Galerkin Approach Leveraging Romanovski–Jacobi Polynomials for Differential Equations

Year: 2025

Type: article

Abstract: This study explores the application of Romanovski–Jacobi polynomials (RJPs) in spectral Galerkin methods (SGMs) for solving differential equations (DEs). It uses a suitable class of modified RJPs as basis functions that meet the homogeneous initial conditions (ICs) given. We derive spectral Galerkin schemes based on modified RJP expansions to solve three models of high-order ordinary differential equations (ODEs) and partial differential equations (PDEs) of first and second orders with ICs. We provide theoretical assurances of the treatment’s efficacy by validating its convergent and error investigations. The method achieves enhanced accuracy, spectral convergence, and computational efficiency. Numerical experiments demonstrate the robustness of this approach in addressing complex physical and engineering problems, highlighting its potential as a powerful tool to obtain accurate numerical solutions for various types of DEs. The findings are compared to those of preceding studies, verifying that our treatment is more effective and precise than that of its competitors.

Source: Mathematics

DOI: 10.3390/math13091461

Authors: Ramy M. Hafez, Mohamed A. Abdelkawy, Hany M. Ahmed

Institutions: Matrouh University, Imam Mohammad ibn Saud Islamic University, Helwan University

Language: English

Topic: Mathematical functions and polynomials

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,137

Funder: Deanship of Scientific Research, Imam Mohammed Ibn Saud Islamic University