An iterative method for solving a boundary value problem for a system of first-order ordinary differential equations with parameter for cluster systems

In this paper, some problems of development, investigation, and implementation of parallel iterative methods for solving nonlinear equations are discussed. The question of finding a self-similar solution of a mathematical model describing the unsteady motion of a gas appeared under the influence of a plane piston in the presence of volume sources (sinks) of mass, impulse, and energy is also considered. The development and implementation of a parallel iterative method for solving the boundary value problem obtained is studied. The work was supported by the International Science and Technology Center (ISTC) in the framework of the project “Development of High-Performance Computing Cluster and Databases in Armenia” (A-823).