ПОСТРОЕНИЕ РЕШЕНИЯ СИСТЕМЫ КВАЗИЛИНЕЙНЫХ УРАВНЕНИЙ МЕТОДОМ ПРОСТОЙ ИТЕРАЦИИ

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This article considers the problem of constructing a solution to a system of quasilinear algebraic equations by the method of simple iteration. The method of simple iteration refers to the type of successive approximations. This method is characterized by the fact that when finding the unknowns in the kth approximation, the values of the unknowns found in the (k-1)-approximation are substituted into the right parts of the initial equations. Attention is paid to the analysis of the iterative process from the point of view of convergence, the region of existence of solutions, as well as the estimation of the error between approximations and the exact solution. As an example, the problem of reducing a system of quasi-linear differential equations with a small parameter to a system of quasi-linear algebraic equations is considered.