Numerical analysis of stochastic oscillators on supercomputers

Abstract

The problem of numerical analysis of stochastic differential equations (SDEs) with oscillating solutions is investigated. The expectation and variance of SDE numerical solutions are shown as functions of the mesh size of integrating the generalized Euler method. Results of some numerical experiments on the simulation of linear and nonlinear stochastic oscillators on the supercomputer of the Siberian Supercomputer Center are presented.

Simulation of the linear mechanical oscillator on GPU

“…In solving numerically the oscillating ordinary differential equations (ODEs), satisfactory accuracy of calculation by the Euler method is usually obtained when 32 integration steps are used per oscillation period (see [26]). …”