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.
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References in zbMATH (referenced in 36 articles )
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Sorted by year (- Pereyra, Marcelo; Mieles, Luis Vargas; Zygalakis, Konstantinos C.: Accelerating proximal Markov chain Monte Carlo by using an explicit stabilized method (2020)
- Komori, Yoshio; Eremin, Alexey; Burrage, Kevin: S-ROCK methods for stochastic delay differential equations with one fixed delay (2019)
- Martín-Vaquero, J.; Kleefeld, A.: ESERK5: a fifth-order extrapolated stabilized explicit Runge-Kutta method (2019)
- Tang, Xiao; Xiao, Aiguo: New explicit stabilized stochastic Runge-Kutta methods with weak second order for stiff Itô stochastic differential equations (2019)
- Abdulle, Assyr; Almuslimani, Ibrahim; Vilmart, Gilles: Optimal explicit stabilized integrator of weak order 1 for stiff and ergodic stochastic differential equations (2018)
- 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)
- Lu, Jianfeng; Spiliopoulos, Konstantinos: Analysis of multiscale integrators for multiple attractors and irreversible Langevin samplers (2018)
- Ben Hammouda, Chiheb; Moraes, Alvaro; Tempone, Raúl: Multilevel hybrid split-step implicit tau-leap (2017)
- Komori, Yoshio; Cohen, David; Burrage, Kevin: Weak second order explicit exponential Runge-Kutta methods for stochastic differential equations (2017)
- 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)
- Guo, Qian; Qiu, Mingming; Mitsui, Taketomo: Asymptotic mean-square stability of explicit Runge-Kutta Maruyama methods for stochastic delay differential equations (2016)
- Haghighi, Amir; Hosseini, Seyed Mohammad; Rößler, Andreas: Diagonally drift-implicit Runge-Kutta methods of strong order one for stiff stochastic differential systems (2016)
- Martín-Vaquero, J.; Kleefeld, B.: Extrapolated stabilized explicit Runge-Kutta methods (2016)
- Carletti, Margherita; Montani, Matteo; Meschini, Valentina; Bianchi, Marzia; Radici, Lucia: Stochastic modelling of PTEN regulation in brain tumors: a model for glioblastoma multiforme (2015)
- Guo, Qian; Zhong, Juan: Almost sure exponential stability of an explicit stochastic orthogonal Runge-Kutta-Chebyshev method for stochastic delay differential equations (2015)
- Reshniak, V.; Khaliq, A. Q. M.; Voss, D. A.; Zhang, G.: Split-step Milstein methods for multi-channel stiff stochastic differential systems (2015)
- Wang, Peng: A-stable Runge-Kutta methods for stiff stochastic differential equations with multiplicative noise (2015)
- Yin, Zhengwei; Gan, Siqing: An improved Milstein method for stiff stochastic differential equations (2015)
- Burrage, Kevin; Lythe, Grant: Accurate stationary densities with partitioned numerical methods for stochastic partial differential equations (2014)
- Komori, Yoshio; Burrage, Kevin: A stochastic exponential Euler scheme for simulation of stiff biochemical reaction systems (2014)