A REFINED GALERKIN APPROACH FOR SOLVING HIGHER-ORDER DIFFERENTIAL EQUATIONS VIA BERNOULLI POLYNOMIALS
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.
Authors
- Alhanouf Alburaikan (ORCID: https://orcid.org/0000-0002-4420-7287)
- Hamiden Abd El‐Wahed Khalifa (ORCID: https://orcid.org/0000-0002-8269-8822)
- Y. H. Youssri (ORCID: https://orcid.org/0000-0003-0403-8797)
- Mohammed Said Touati Brahim (ORCID: https://orcid.org/0000-0002-1345-8067)
- Ramy M. Hafez (ORCID: https://orcid.org/0000-0001-9533-3171)
- Taha Radwan (ORCID: https://orcid.org/0000-0003-1466-8821)
Institutions
- Cairo University (EG)
- Qassim University (SA)
- Egypt Nanotechnology Center (EG)
- Centre Hospitalo-Universitaire Bab El Oued (DZ)
Publication Details
- Journal
- Fractals
- Published
- 2025-01-01
- DOI
- https://doi.org/10.1142/s0218348x25401838
- Citations
- 3
- Primary Topic
- Numerical methods for differential equations
- Type
- article
- Field-Weighted Citation Impact
- 7.89