In this paper we consider mathematical models of some problems of natural science, for example, self-similarity problems of gas-dynamics giving rise to boundary problems of first order ordinary differential equations (ODE) with one parameter. The boundary problems of first order ODE with one parameter are considered in [1, 2], where iterative methods based on the implementation of Newton's Method, are presented. Next, an iterative method for solving the boundary value problem of the first order system of ODE with one parameter on a multiprocessor type SIMD [3] is shown. The convergence of this process is proved and the speed of convergence is estimated. The feasibility of this method is illustrated for the one dimensional instability movement of gas arising from the movement of the piston in presence of a volume source (volume channel) of mass, impulse and energy in gas. Finally the results are given.

http://atarazanas.sci.uma.es/docs/articulos/16669885.pdf

On one numerical method for solving some self-similarityproblems of gas-dynamics on a multiprocessor

New explicit group S.O.R. methods suitable for use on an asynchronous MIMD computer are presented for the numerical solution of the sparse linear systems derived from the discretization of two-dimensional, second-order, elliptic boundary value problems. A comparison with existing implicit line S.O.R. schemes for the Dirichlet model problem shows the new schemes to be superior (Barlow and Evans, 1982).

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Parallel S.O.R. iterative methods

Parallel Processing Systems

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On one numerical method for solving some self-similarityproblems of gas-dynamics on a multiprocessor

Parallel S.O.R. iterative methods

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