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

Abstract

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.

Keywords:

• Newton‘s method
• Cauchy's problem
• Chord‘s method
• Interpolation formulae

Computer Reviews C.R. Categories:

• G.1.5 [Numerical Analysis]
• Roots of Nonlinear Equations: Convergence
• Iterative Methods
• G.1.7 [Numerical Analysis]: Ordinary differential Equations Boundary value problems
• 5.2 [Physical Sciences and Engineering]