Numerical Solutions for non-Markovian Stochastic Equations of Motion

TL;DR

This paper evaluates the accuracy of numerical solutions for non-Markovian stochastic equations by comparing them with analytical solutions and examining different transformation methods to ensure reliability.

Contribution

It provides an assessment of the reliability of standard numerical methods, like Runge-Kutta, for solving non-Markovian stochastic equations through comparison with analytical solutions.

Findings

Numerical solutions closely match analytical results.

Different transformation prescriptions affect solution accuracy.

Runge-Kutta method proves reliable for these equations.

Abstract

The reliability and precision of numerically solving stochastic non-Markovian equations by standard numerical codes, more specifically, with the fourth-order Runge-Kutta routine for solving differential equations, is gauged by comparing the results obtained from analytical solutions for the equations. The results for different prescriptions for transforming the non-Markovian equations in a system of Markovian ones are compared so to check the reliability of the numerical method.