A COMPREHENSIVE STUDY ON SOLVING MULTITYPE DIFFERENTIAL EQUATIONS USING ROMANOVSKI–JACOBI MATRIX METHODS

Ramy Hafez (), Mohamed Haiour (), Seham Tantawy, Alhanouf Alburaikan () and Hamiden Khalifa ()
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Ramy Hafez: Department of Mathematics, Faculty of Education, Matrouh University, Marsa Matrouh 51511, Egypt
Mohamed Haiour: Numerical Analysis, Optimization and Statistics Laboratory, University Badji Mokhtar, Annaba 23000, Algeria
Seham Tantawy: Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia
Alhanouf Alburaikan: Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia
Hamiden Khalifa: Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia

FRACTALS (fractals), 2025, vol. 33, issue 08, 1-10

Abstract: This research presents advanced spectral algorithms based on Romanovski–Jacobi polynomials for solving various types of differential equations. The study explores the integration of these polynomials into pseudospectral methods, enabling efficient handling of higher-order ordinary differential equations (ODEs) and second-order linear partial differential equations (PDEs). The proposed methods leverage the operational matrices of derivatives to transform differential equations into systems of algebraic equations, ensuring high accuracy and rapid convergence. Numerical experiments validate the effectiveness of the algorithms in solving problems with complex geometries and boundary conditions. The results demonstrate the superiority of Romanovski–Jacobi-based techniques compared to traditional spectral methods, offering a robust and versatile framework for scientific and engineering applications.

Keywords: Romanovski–Jacobi Polynomials; Numerical Methods; Efficiency; Algorithms; Collocation Points; Higher-Order Differential Equations; Second-Order Linear PDEs; Operational Matrix (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S0218348X25401528

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