S-ROCK: Chebyshev Methods for Stiff Stochastic Differential Equations

Authors:
Assyr Abdulle;Stephane Cirilli
Affiliations:
-;-
Venue:
SIAM Journal on Scientific Computing
Year:
2008

Citing 0
Cited 8

Physically consistent simulation of mesoscale chemical kinetics: The non-negative FIS-α method

Journal of Computational Physics
Partitioned Runge-Kutta-Chebyshev Methods for Diffusion-Advection-Reaction Problems

SIAM Journal on Scientific Computing
Numerical methods for stochastic partial differential equations with multiple scales

Journal of Computational Physics
Weak second order S-ROCK methods for Stratonovich stochastic differential equations

Journal of Computational and Applied Mathematics
Strong first order S-ROCK methods for stochastic differential equations

Journal of Computational and Applied Mathematics
PIROCK: A swiss-knife partitioned implicit-explicit orthogonal Runge-Kutta Chebyshev integrator for stiff diffusion-advection-reaction problems with or without noise

Journal of Computational Physics
Stabilized multilevel Monte Carlo method for stiff stochastic differential equations

Journal of Computational Physics
Stabilized explicit Runge-Kutta methods for multi-asset American options

Computers & Mathematics with Applications

Quantified Score

Hi-index	0.02

Visualization

Abstract

We present and analyze a new class of numerical methods for the solution of stiff stochastic differential equations (SDEs). These methods, called S-ROCK (for stochastic orthogonal Runge-Kutta Chebyshev), are explicit and of strong order 1 and possess large stability domains in the mean-square sense. For mean-square stable stiff SDEs, they are much more efficient than the standard explicit methods proposed so far for stochastic problems and give significant speed improvement. The explicitness of the S-ROCK methods allows one to handle large systems without linear algebra problems usually encountered with implicit methods. Numerical results and comparisons with existing methods are reported.