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.

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  1. Ben Hammouda, Chiheb; Moraes, Alvaro; Tempone, Raúl: Multilevel hybrid split-step implicit tau-leap (2017)
  2. 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)
  3. Guo, Qian; Qiu, Mingming; Mitsui, Taketomo: Asymptotic mean-square stability of explicit Runge-Kutta Maruyama methods for stochastic delay differential equations (2016)
  4. Haghighi, Amir; Hosseini, Seyed Mohammad; Rößler, Andreas: Diagonally drift-implicit Runge-Kutta methods of strong order one for stiff stochastic differential systems (2016)
  5. Martín-Vaquero, J.; Kleefeld, B.: Extrapolated stabilized explicit Runge-Kutta methods (2016)
  6. Carletti, Margherita; Montani, Matteo; Meschini, Valentina; Bianchi, Marzia; Radici, Lucia: Stochastic modelling of PTEN regulation in brain tumors: a model for glioblastoma multiforme (2015)
  7. Reshniak, V.; Khaliq, A.Q.M.; Voss, D.A.; Zhang, G.: Split-step Milstein methods for multi-channel stiff stochastic differential systems (2015)
  8. Wang, Peng: A-stable Runge-Kutta methods for stiff stochastic differential equations with multiplicative noise (2015)
  9. Burrage, Kevin; Lythe, Grant: Accurate stationary densities with partitioned numerical methods for stochastic partial differential equations (2014)
  10. Komori, Yoshio; Burrage, Kevin: A stochastic exponential Euler scheme for simulation of stiff biochemical reaction systems (2014)
  11. Martín-Vaquero, J.; Khaliq, A.Q.M.; Kleefeld, B.: Stabilized explicit Runge-Kutta methods for multi-asset American options (2014)
  12. Abdulle, Assyr; Blumenthal, Adrian: Stabilized multilevel Monte Carlo method for stiff stochastic differential equations (2013)
  13. 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)
  14. Abdulle, Assyr; Vilmart, Gilles; Zygalakis, Konstantinos C.: Weak second-order explicit stabilized methods for stiff stochastic differential equations (2013)
  15. 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)
  16. Kleefeld, B.; Martín-Vaquero, J.: SERK2v2: A new second-order stabilized explicit Runge-Kutta method for stiff problems (2013)
  17. Abdulle, A.; Pavliotis, G.A.: Numerical methods for stochastic partial differential equations with multiple scales (2012)
  18. Abdulle, Assyr; Cohen, David; Vilmart, Gilles; Zygalakis, Konstantinos C.: High weak order methods for stochastic differential equations based on modified equations (2012)
  19. Alcock, Jamie; Burrage, Kevin: Stable strong order 1.0 schemes for solving stochastic ordinary differential equations (2012)
  20. Komori, Yoshio; Burrage, Kevin: Weak second order S-ROCK methods for Stratonovich stochastic differential equations (2012)

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