Work

A Refined Galerkin Approach for Solving Higher-order Differential Equations Via Bernoulli Polynomials

Year: 2025

Type: article

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.

Source: Fractals

DOI: 10.1142/s0218348x25401838

Authors: MOHAMMED SAID TOUATI BRAHIM, YOUSSRI HASSAN YOUSSRI, ALHANOUF ALBURAIKAN, HAMIDEN KHALIFA, TAHA RADWN, RAMY HAFEZ

Institutions: University of Eloued, Cairo University, Qassim University, Matrouh University

Language: English

Topic: Mathematical functions and polynomials

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Funder: Qassim University

OpenAlex ID: W4409359209

FWCI: 7.505

Cites: 18

Cited by: 4

Related to: 10