Probabilistic aspects of "computer analogy" method for solving differential equations

Probabilistic aspects of "computer analogy" method for solving differential equations

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Method which allows to obtain explicit form of the solution as a part of power series of the argument step is developed.Formalization of characteristics of the algorithm analogous to operations Blue Bottle Lamp Gift Box of a computer is performed.The operation of transfer from one rank to another leads to a probability scheme Rattles of the algorithm that averages unknown intermediate steps in higher ranks of the series.The stochastic characteristics of the method are studied and illustrated.

Examples of solving nonlinear equations and systems of nonlinear differential equations are presented.