S-ROCK

S-ROCK: Chebyshev methods for stiff stochastic differential equations. 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.


References in zbMATH (referenced in 20 articles )

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  1. Guo, Qian; Qiu, Mingming; Mitsui, Taketomo: Asymptotic mean-square stability of explicit Runge-Kutta Maruyama methods for stochastic delay differential equations (2016)
  2. Haghighi, Amir; Hosseini, Seyed Mohammad; Rößler, Andreas: Diagonally drift-implicit Runge-Kutta methods of strong order one for stiff stochastic differential systems (2016)
  3. Reshniak, V.; Khaliq, A.Q.M.; Voss, D.A.; Zhang, G.: Split-step Milstein methods for multi-channel stiff stochastic differential systems (2015)
  4. Wang, Peng: A-stable Runge-Kutta methods for stiff stochastic differential equations with multiplicative noise (2015)
  5. Burrage, Kevin; Lythe, Grant: Accurate stationary densities with partitioned numerical methods for stochastic partial differential equations (2014)
  6. Komori, Yoshio; Burrage, Kevin: A stochastic exponential Euler scheme for simulation of stiff biochemical reaction systems (2014)
  7. Martín-Vaquero, J.; Khaliq, A.Q.M.; Kleefeld, B.: Stabilized explicit Runge-Kutta methods for multi-asset American options (2014)
  8. Abdulle, Assyr; Vilmart, Gilles: PIROCK: A swiss-knife partitioned implicit-explicit orthogonal Runge-Kutta Chebyshev integrator for stiff diffusion-advection-reaction problems with or without noise (2013)
  9. Abdulle, Assyr; Vilmart, Gilles; Zygalakis, Konstantinos C.: Weak second-order explicit stabilized methods for stiff stochastic differential equations (2013)
  10. Abdulle, A.; Vilmart, G.; Zygalakis, K.C.: Mean-square $A$-stable diagonally drift-implicit integrators of weak second order for stiff It^o stochastic differential equations (2013)
  11. Abdulle, A.; Pavliotis, G.A.: Numerical methods for stochastic partial differential equations with multiple scales (2012)
  12. Abdulle, Assyr; Cohen, David; Vilmart, Gilles; Zygalakis, Konstantinos C.: High weak order methods for stochastic differential equations based on modified equations (2012)
  13. Alcock, Jamie; Burrage, Kevin: Stable strong order 1.0 schemes for solving stochastic ordinary differential equations (2012)
  14. Komori, Yoshio; Burrage, Kevin: Weak second order S-ROCK methods for Stratonovich stochastic differential equations (2012)
  15. Dana, Saswati; Raha, Soumyendu: Physically consistent simulation of mesoscale chemical kinetics: The non-negative FIS-$\alpha$ method (2011)
  16. Zbinden, Christophe J.: Partitioned Runge-Kutta-Chebyshev methods for diffusion-advection-reaction problems (2011)
  17. Tao, Molei; Owhadi, Houman; Marsden, Jerrold E.: Nonintrusive and structure preserving multiscale integration of stiff ODEs, SDEs, and Hamiltonian systems with hidden slow dynamics via flow averaging (2010)
  18. Wang, P.; Liu, Zhenxin: Stabilized Milstein type methods for stiff stochastic systems (2009)
  19. Abdulle, Assyr; Cirilli, Stephane: S-ROCK: Chebyshev methods for stiff stochastic differential equations (2008)
  20. Abdulle, Assyr; Cirilli, Stéphane: Stabilized methods for stiff stochastic systems (2007)