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 36 articles )

Showing results 1 to 20 of 36.
Sorted by year (citations)

1 2 next

  1. Pereyra, Marcelo; Mieles, Luis Vargas; Zygalakis, Konstantinos C.: Accelerating proximal Markov chain Monte Carlo by using an explicit stabilized method (2020)
  2. Komori, Yoshio; Eremin, Alexey; Burrage, Kevin: S-ROCK methods for stochastic delay differential equations with one fixed delay (2019)
  3. Martín-Vaquero, J.; Kleefeld, A.: ESERK5: a fifth-order extrapolated stabilized explicit Runge-Kutta method (2019)
  4. Tang, Xiao; Xiao, Aiguo: New explicit stabilized stochastic Runge-Kutta methods with weak second order for stiff Itô stochastic differential equations (2019)
  5. Abdulle, Assyr; Almuslimani, Ibrahim; Vilmart, Gilles: Optimal explicit stabilized integrator of weak order 1 for stiff and ergodic stochastic differential equations (2018)
  6. Bocher, Philippe; Montijano, Juan I.; Rández, Luis; Van Daele, Marnix: Explicit Runge-Kutta methods for stiff problems with a gap in their eigenvalue spectrum (2018)
  7. Lu, Jianfeng; Spiliopoulos, Konstantinos: Analysis of multiscale integrators for multiple attractors and irreversible Langevin samplers (2018)
  8. Ben Hammouda, Chiheb; Moraes, Alvaro; Tempone, Raúl: Multilevel hybrid split-step implicit tau-leap (2017)
  9. Komori, Yoshio; Cohen, David; Burrage, Kevin: Weak second order explicit exponential Runge-Kutta methods for stochastic differential equations (2017)
  10. Mora, C. M.; Mardones, H. A.; Jimenez, J. C.; Selva, M.; Biscay, Rolando: A stable numerical scheme for stochastic differential equations with multiplicative noise (2017)
  11. Guo, Qian; Qiu, Mingming; Mitsui, Taketomo: Asymptotic mean-square stability of explicit Runge-Kutta Maruyama methods for stochastic delay differential equations (2016)
  12. Haghighi, Amir; Hosseini, Seyed Mohammad; Rößler, Andreas: Diagonally drift-implicit Runge-Kutta methods of strong order one for stiff stochastic differential systems (2016)
  13. Martín-Vaquero, J.; Kleefeld, B.: Extrapolated stabilized explicit Runge-Kutta methods (2016)
  14. Carletti, Margherita; Montani, Matteo; Meschini, Valentina; Bianchi, Marzia; Radici, Lucia: Stochastic modelling of PTEN regulation in brain tumors: a model for glioblastoma multiforme (2015)
  15. Guo, Qian; Zhong, Juan: Almost sure exponential stability of an explicit stochastic orthogonal Runge-Kutta-Chebyshev method for stochastic delay differential equations (2015)
  16. Reshniak, V.; Khaliq, A. Q. M.; Voss, D. A.; Zhang, G.: Split-step Milstein methods for multi-channel stiff stochastic differential systems (2015)
  17. Wang, Peng: A-stable Runge-Kutta methods for stiff stochastic differential equations with multiplicative noise (2015)
  18. Yin, Zhengwei; Gan, Siqing: An improved Milstein method for stiff stochastic differential equations (2015)
  19. Burrage, Kevin; Lythe, Grant: Accurate stationary densities with partitioned numerical methods for stochastic partial differential equations (2014)
  20. Komori, Yoshio; Burrage, Kevin: A stochastic exponential Euler scheme for simulation of stiff biochemical reaction systems (2014)

1 2 next