Algorithm for solving the linear Cauchy problem for large systems of ordinary differential equations with the use of parallel computations

Moryakov A. V.

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Algorithm for solving the linear Cauchy problem for large systems of ordinary differential equations with the use of parallel computations

机译：用平行计算解决常微分方程大型系统的线性Cauchy问题的算法

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An algorithm for solving the linear Cauchy problem for large systems of ordinary differential equations is presented. The algorithm for systems of first-order differential equations is implemented in the EDELWEISS code with the possibility of parallel computations on supercomputers employing the MPI (Message Passing Interface) standard for the data exchange between parallel processes. The solution is represented by a series of orthogonal polynomials on the interval [0, 1]. The algorithm is characterized by simplicity and the possibility to solve nonlinear problems with a correction of the operator in accordance with the solution obtained in the previous iterative process.

机译：介绍了一种解决常规方程大型系统线性CAUCHY问题的算法。在EDELWEIS码中实现了一阶微分方程系统的算法，其在采用PANDASS处理的数据交换的超级计算机上的超级计算机上的并行计算的可能性。该解决方案由间隔的一系列正交多项式表示[0,1]。该算法的特征在于简单性，并且可以根据在先前迭代过程中获得的解决方案来解决操作员校正的非线性问题的可能性。

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来源
《Physics of atomic nuclei》 |2016年第8期|共9页
作者
Moryakov A. V.;
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作者单位

Kurchatov Inst Natl Res Ctr Pl Akad Kurchatova 1 Moscow 123182 Russia;

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原文格式 PDF
正文语种 eng
中图分类原子物理学;原子核物理学、高能物理学;
关键词
algorithm; iterative process; program; system of equations; solution; space; vector;

机译：算法;迭代过程;程序;方程式;解决方案;空间;向量;

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1. Algorithm for solving the linear Cauchy problem for large systems of ordinary differential equations with the use of parallel computations [J] . Moryakov A. V. Physics of atomic nuclei . 2016,第8期

机译：用平行计算解决常微分方程大型系统的线性Cauchy问题的算法
2. Algorithm for solving the linear Cauchy problem for large systems of ordinary differential equations with the use of parallel computations [J] . A. V. Moryakov Physics of atomic nuclei . 2016,第8期

机译：用平行计算解决常微分方程大型系统的线性Cauchy问题的算法
3. 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 [J] . Physics of atomic nuclei . 2019,第8期

机译：用溶液作为正交多项式的扩展膨胀的一阶常微分方程大型系统的线性CAUCHY问题解决方案的平行算法的收敛估计
4. Parallel Implementation of Fourth Order Block Backward Differentiation Formulas for Solving System of Stiff Ordinary Differential Equations [C] . Zarina Bibi Ibrahim, Nor Ain Azeany Mohd Nasir, Khairil Iskandar Othman, National Symposium on Mathematical Sciences . 2013

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5. Parallel algorithms and software for time-dependent systems of nonlinear partial differential equations with an application in computational biology. [D] . Murillo, Maria Silva. 2002

机译：非线性偏微分方程时间相关系统的并行算法和软件及其在计算生物学中的应用。
6. Contribution to Speeding-Up the Solving of Nonlinear Ordinary Differential Equations on Parallel/Multi-Core Platforms for Sensing Systems [O] . Vahid Tavakkoli, Kabeh Mohsenzadegan, Jean Chamberlain Chedjou, 2020

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7. A numerical method for solving the Cauchy problem for systems of ordinary differential equations by means of a system orthogonal in the sense of Sobolev generated by the cosine system [O] . Idris Sharapudinov, Magomedrasul Magomed-Kasumov 2017

机译：通过余弦系统生成的SoboLev意义上的系统正交解决常微分方程系统的Cauchy问题的数值方法
8. Efficient Algorithms for Solving Systems of Ordinary Differential Equations for Ecosystem Modeling [R] . Malanchuk, J. , Otis, J. , Bouver, H. 1980

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Algorithm for solving the linear Cauchy problem for large systems of ordinary differential equations with the use of parallel computations

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