Presentations

Appliaction of computer analogy method to the solution of systems of differential equations

Aristov V.V., Muzyka A.A.¹, Stroganov A.V.

Federal Research Center Informatics and Control of the Russian Academy of Sciences, Russia, 119333, Moscow, Vavilova St., 42, building 2, Tel.: +7 (499) 135-62-60, Fax: +7 (495) 930-45-05, E-mail: aristovvl@yandex.ru

¹Federal State Budgetary Educational Institution of Higher Education “MIREA – Russian Technological University”, Russia, 119454, Moscow, Vernadsky Avenue, Building 78, Tel.: +7 499 600-80-80, Fax: +7 499 434-92-87, E-mail: vispoftheblayor@gmail.com

The paper [1] proposed a method for constructing solutions to differential equations using an analogy with the operation of a computer. This approach eliminates intermediate steps in recurrent formulas of difference schemes for solving differential equations. For this purpose, the main properties of a digital computer are formalized - a fixed number of digits and a transfer from one digit to the next. The solution is obtained as a segment of a series in powers of the argument step.

This approach can be used to construct solutions to systems of nonlinear equations, in particular to construct solutions to complex Lorenz, Rössler, and Shimizu-Morioka systems. The formulas for the coefficients of the series take the form of a linear congruential generator, which allows us to consider the coefficients at higher powers as pseudorandom. Approximating the coefficients at higher powers using normally or uniformly distributed random variables allows us to obtain an explicit solution to the problem.

References 1. Aristov, V.V., Stroganov, A.V.: A method of formalizing computer operations for solving nonlinear differential equations. Applied Mathematics and Computation. 2012, Vol. 218, p. 8083-8089.

• abstract in Russian (PDF)