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A Novel Method for Solving Second Kind Volterra Integral Equations with Discontinuous Kernel

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  • Samad Noeiaghdam

    (Industrial Mathematics Laboratory, Baikal School of BRICS, Irkutsk National Research Technical University, 664074 Irkutsk, Russia
    Department of Applied Mathematics and Programming, South Ural State University, Lenin Prospect 76, 454080 Chelyabinsk, Russia)

  • Sanda Micula

    (Department of Mathematics and Computer Science, Babeş-Bolyai University, 400084 Cluj-Napoca, Romania)

Abstract

Load leveling problems and energy storage systems can be modeled in the form of Volterra integral equations (VIE) with a discontinuous kernel. The Lagrange–collocation method is applied for solving the problem. Proving a theorem, we discuss the precision of the method. To control the accuracy, we apply the CESTAC (Controle et Estimation Stochastique des Arrondis de Calculs) method and the CADNA (Control of Accuracy and Debugging for Numerical Applications) library. For this aim, we apply discrete stochastic mathematics (DSA). Using this method, we can control the number of iterations, errors and accuracy. Additionally, some numerical instabilities can be identified. With the aid of this theorem, a novel condition is used instead of the traditional conditions.

Suggested Citation

  • Samad Noeiaghdam & Sanda Micula, 2021. "A Novel Method for Solving Second Kind Volterra Integral Equations with Discontinuous Kernel," Mathematics, MDPI, vol. 9(17), pages 1-12, September.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:17:p:2172-:d:629572
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    References listed on IDEAS

    as
    1. Vignes, J., 1993. "A stochastic arithmetic for reliable scientific computation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 35(3), pages 233-261.
    2. Ravi P. Agarwal & Sadek Gala & Maria Alessandra Ragusa, 2020. "A Regularity Criterion in Weak Spaces to Boussinesq Equations," Mathematics, MDPI, vol. 8(6), pages 1-11, June.
    3. Luo, Wei-Hua & Gu, Xian-Ming & Yang, Liu & Meng, Jing, 2021. "A Lagrange-quadratic spline optimal collocation method for the time tempered fractional diffusion equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 1-24.
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