Abstract
This paper is devoted to the algorithm of the linear Cauchy problem solution for large systems of first-order ordinary differential equations using parallel calculations. The proof of the convergence of the iteration process using the solution as expansion over orthogonal polynomials for the interval [0,1] is presented. The features of this algorithm are its simplicity, the opportunity to get a solution by parallel calculations, and also the possibility to get a solution for nonlinear problems by changing the operator using the solution from the iteration process.
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Russian Text © The Author(s), 2018, published in Voprosy Atomnoi Nauki i Tekhniki. Seriya: Fizika Yadernykh Reaktorov, 2018, No. 1, pp. 4–9.
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Moryakov, A.V. The Convergence Estimation of the Parallel Algorithm of the Linear Cauchy Problem Solution for Large Systems of First-Order Ordinary Differential Equations Using the Solution as Expansion over Orthogonal Polynomials. Phys. Atom. Nuclei 82, 1077–1081 (2019). https://doi.org/10.1134/S1063778819080131
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DOI: https://doi.org/10.1134/S1063778819080131