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


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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.

About the authors

A. V. Moryakov

National Research Center Kurchatov Institute

Author for correspondence.
Email: sailor@orc.ru
Russian Federation, Moscow, 123182

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