Weak second-order explicit stabilized methods for stiff stochastic differential equations. (English) Zbl 1281.65005
Second-order orthogonal Runge-Kutta-Chebyshev methods for stiff deterministic ordinary differential equations are generalized and modified to apply to systems of stiff stochastic differential equations (SSDE) of the form
\[
dX(t)= f(X(t))\,dt+ \sum^m_{r=1} g^r(X(t))\,dW_r(t),\quad X(0)= X_0,
\]
where the \(W_r(t)\) are independent one-dimensional Wiener processes. An explicit method, denoted S-ROCK2, is derived and shown to have weak second-order convergence. Its numerical asymptotic stability domain and its numerical mean-square stability domain are found, and its stability properties are shown to compare favorably to those of other methods for SSDE. Results of numerical experiments are presented that demonstrate the advantages of S-ROCK2.
Reviewer: Melvin D. Lax (Long Beach)
MSC:
65C30 | Numerical solutions to stochastic differential and integral equations |
60H35 | Computational methods for stochastic equations (aspects of stochastic analysis) |
65L20 | Stability and convergence of numerical methods for ordinary differential equations |
60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
65L04 | Numerical methods for stiff equations |
34F05 | Ordinary differential equations and systems with randomness |
65L06 | Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations |