Comparative analysis of computational methods of system of nonlinear equations

The consideration of numerous applied problems leads to systems of nonlinear equations, they include boundary problems for ordinary differential equations and partial differential equations (solved by the finite difference method), optimization problems, problems of minimization of functions of many variables, the use of implicit methods for integrating ordinary differential equations, etc. Numerical solution of systems of nonlinear equations in the general case is a more complicated problem than the solution of systems of linear equations, since there are no methods that guarantee the success of solving any problem of this kind. Identifying the optimal method and its further selection allows you to increase the chances of successfully solving systems of nonlinear equations. In connection with the relevance of the above-mentioned, this article presents the algorithms for methods for the numerical solution of systems of nonlinear equations, according to which the root of a typical system for applied problems was searched. According to the obtained results, a comparative analysis was conducted in order to identify the optimal method. The optimal method is the one that found the values of all the roots of the system with the required accuracy in the least number of iterations.