A REFINED GALERKIN APPROACH FOR SOLVING HIGHER-ORDER DIFFERENTIAL EQUATIONS VIA BERNOULLI POLYNOMIALS

Mohammed Said Touati Brahim, Youssri Hassan Youssri (), Alhanouf Alburaikan (), Hamiden Khalifa (), Taha Radwn and Ramy Hafez ()
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Mohammed Said Touati Brahim: Laboratory of Operator Theory and EDP
Youssri Hassan Youssri: Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, Egypt
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
Taha Radwn: Department of Management Information Systems, College of Business and Economics, Qassim University, Buraydah 51452, Saudi Arabia
Ramy Hafez: Department of Mathematics, Faculty of Education, Matrouh University, Marsa Matrouh 51511, Egypt

FRACTALS (fractals), 2025, vol. 33, issue 08, 1-14

Abstract: This paper introduces a novel Galerkin algorithm, employing Bernoulli polynomials, to efficiently solve high-order differential equations and systems with homogeneous and nonhomogeneous initial conditions. The algorithm’s efficacy hinges on the strategic selection of trial functions that align with the problem’s initial conditions. Illustrative examples validate the proposed algorithm’s validity and efficiency. Comparative analyses against existing spectral methods emphasize the superior performance of the new algorithm.

Keywords: Bernoulli Polynomials; Spectral Methods; High-Order Differential Equations; Numerical Methods (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S0218348X25401838

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