Three-stage stochastic Runge-Kutta methods for stochastic differential equations
Two stochastic Runge-Kutta methods with strong order of convergence 1 (one a three-stage explicit scheme, the other a three-stage semi-implicit scheme) are devised for approximating the strong solution of the \(m\)-dimensional Stratonovich stochastic differential equation \[ dy(t) =f(y(t))dt+g(y(t))\circ dW(t),\quad y(t_0)=y_0 \] where \(W(t)\) is a Wiener process. Their respective regions of MS-stability are studied. Numerical results are summarized for two examples to demonstrate the favorable accuracy of the methods.
Stratonovich stochastic differential equation
scientific article; zbMATH DE number 5368371