Numerical integration methods for stochastic wave function equations
Four methods for numerically solving stochastic differential equations (SDEs) are compared for two examples from quantum mechanics of open systems. The methods examined are the Euler-Maruyama scheme, a stochastic Heun scheme, a stochastic Runge-Kutta order 4 scheme, and an explicit order 2 weak scheme due to Platen [cf. \textit{P. E. Kloeden} and \textit{E. Platen}, Numerical solution of stochastic differential equations (1992; Zbl 0752.60043)]. The examples are an SDE arising from a damped harmonic oscillator and an SDE arising from a two-level atom driven by an external single mode laser field on resonance. It is found that Platen's method yields the best results, especially when comparing accuracy per unit of CPU time required; and that the stochastic Heun and stochastic Runge-Kutta methods have no significant advantage over the Euler-Maruyama method.
scientific article; zbMATH DE number 1552645