SOLUTION OF DIFFERENTIAL EQUATIONS AND SYSTEMS OF DIFFERENTIAL EQUATIONS WITH THE USE OF MULTIPROCESSOR COMPUTERS

Abstract

The paper proposes computational methods for solving differential equations and systems of two differential equations with initial conditions. At the beginning of the article the statement of the problem is given. Then we propose an essential complement to the classical methods for solving the Cauchy problem, which gives a new indication of the correctness of the estimation of the functionsolution. This feature is based on the geometric construction of the solution of several Cauchy problems that differ only in the initial conditions. The article describes an algorithm for constructing a solution on the investigated interval. After that, the possibility of generalizing a feature to systems of two differential equations is described, when the solution is not just a function but a function in space. The methods themselves are easily parallelized, therefore, they can effectively use multiprocessor computers.