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A Refined Galerkin Approach For Solving Higher-Order Differential Equations Via Bernoulli Polynomials

Author

Listed:
  • 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)

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.

Suggested Citation

  • Mohammed Said Touati Brahim & Youssri Hassan Youssri & Alhanouf Alburaikan & Hamiden Khalifa & Taha Radwn & Ramy Hafez, 2025. "A Refined Galerkin Approach For Solving Higher-Order Differential Equations Via Bernoulli Polynomials," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 33(08), pages 1-14.
    • Handle: RePEc:wsi:fracta:v:33:y:2025:i:08:n:s0218348x25401838
    DOI: 10.1142/S0218348X25401838
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