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

Samad Noeiaghdam and Sanda Micula
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Samad Noeiaghdam: Industrial Mathematics Laboratory, Baikal School of BRICS, Irkutsk National Research Technical University, 664074 Irkutsk, Russia
Sanda Micula: Department of Mathematics and Computer Science, Babeş-Bolyai University, 400084 Cluj-Napoca, Romania

Mathematics, 2021, vol. 9, issue 17, 1-12

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.

Keywords: Volterra integral equations; Lagrange–collocation method; discrete stochastic mathematics; CESTAC method; CADNA library (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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