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A Novel Projection Method for Cauchy-Type Systems of Singular Integro-Differential Equations

Author

Listed:
  • Saeed Althubiti

    (Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia
    These authors contributed equally to this work.)

  • Abdelaziz Mennouni

    (Department of Mathematics, LTM, University of Batna 2, Mostefa Ben Boulaïd, Fesdis, Batna 05078, Algeria
    These authors contributed equally to this work.)

Abstract

This article introduces a new projection method via shifted Legendre polynomials and an efficient procedure for solving a system of integro-differential equations of the Cauchy type. The proposed computational process solves two systems of linear equations. We demonstrate the existence of the solution to the approximate problem and conduct an error analysis. Numerical tests provide theoretical results.

Suggested Citation

  • Saeed Althubiti & Abdelaziz Mennouni, 2022. "A Novel Projection Method for Cauchy-Type Systems of Singular Integro-Differential Equations," Mathematics, MDPI, vol. 10(15), pages 1-11, July.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:15:p:2694-:d:875870
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    References listed on IDEAS

    as
    1. Dauylbayev, M.K. & Uaissov, B., 2020. "Integral boundary-value problem with initial jumps for a singularly perturbed system of integrodifferential equations," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    2. Edyta Hetmaniok & Mariusz Pleszczyński, 2022. "Comparison of the Selected Methods Used for Solving the Ordinary Differential Equations and Their Systems," Mathematics, MDPI, vol. 10(3), pages 1-15, January.
    Full references (including those not matched with items on IDEAS)

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    Cited by:

    1. Abdelkader Moumen & Abdelaziz Mennouni & Mohamed Bouye, 2023. "A Novel Vieta–Fibonacci Projection Method for Solving a System of Fractional Integrodifferential Equations," Mathematics, MDPI, vol. 11(18), pages 1-14, September.
    2. Rais Ahmad & Mohd Ishtyak & Arvind Kumar Rajpoot & Yuanheng Wang, 2022. "Solving System of Mixed Variational Inclusions Involving Generalized Cayley Operator and Generalized Yosida Approximation Operator with Error Terms in q -Uniformly Smooth Space," Mathematics, MDPI, vol. 10(21), pages 1-17, November.
    3. Abdelkader Moumen & Abdelaziz Mennouni, 2022. "A New Projection Method for a System of Fractional Cauchy Integro-Differential Equations via Vieta–Lucas Polynomials," Mathematics, MDPI, vol. 11(1), pages 1-14, December.

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