S-ROCK swMATH ID: 11792 Software Authors: Abdulle, Assyr; Cirilli, Stephane Description: 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. Homepage: http://epubs.siam.org/doi/abs/10.1137/070679375 Keywords: stiff problems; stochastic differential equations; mean-square stability; Chebyshev methods; Runge-Kutta methods; explicit methods Related Software: RODAS; RKC; PIROCK; SERK2; MEBDF; SERK2v3; Matlab; MersenneTwister; Mathematica; MuPAD; RRR; BUQO; MATLAB ODE suite; ode23s; ode113; Ode15s; ode45; ode23; DASSL; VODE Cited in: 43 Publications all top 5 Cited by 65 Authors 9 Abdulle, Assyr 7 Burrage, Kevin 7 Vilmart, Gilles 5 Komori, Yoshio 5 Zygalakis, Konstantinos C. 4 Martín-Vaquero, Jesús 3 Kleefeld, B. 2 Almuslimani, Ibrahim 2 Cirilli, Stéphane 2 Guo, Qian 2 Haghighi, Amir 2 Khaliq, Abdul Q. M. 2 Rößler, Andreas 2 Samaey, Giovanni 2 Vandecasteele, Hannes S. 2 Wang, Peng 2 Zielinski, Przemyslaw 1 Alcock, Jamie 1 Ben Hammouda, Chiheb 1 Bianchi, Marzia 1 Biscay, Rolando J. 1 Blumenthal, Adrian 1 Bocher, Philippe 1 Burrage, Pamela M. 1 Carletti, Margherita 1 Dana, Saswati 1 Ding, Xiaohua 1 Eftekhari, Armin 1 Eremin, Alexey S. 1 Gan, Siqing 1 Hosseini, Seyed Mohammad 1 Jimenez, Juan Carlos 1 Kleefeld, Andreas 1 Liu, Zhenxin 1 Lu, Jianfeng 1 Lythe, Grant 1 Mardones, H. A. 1 Marsden, Jerrold Eldon 1 Meschini, Valentina 1 Mieles, Luis Vargas 1 Mitsui, Taketomo 1 Montani, Matteo 1 Montijano, Juan Ignacio 1 Mora, Carlos M. 1 Moraes, Alvaro 1 Owhadi, Houman 1 Pavliotis, Grigorios A. 1 Pereyra, Marcelo 1 Qiu, Mingming 1 Radici, Lucia 1 Raha, Soumyendu 1 Rández, Luis 1 Reshniak, Viktor 1 Spiliopoulos, Konstantinos V. 1 Tang, Xiao 1 Tao, Molei 1 Tempone, Raúl F. 1 Van Daele, Marnix 1 Vandereycken, Bart 1 Voss, David A. 1 Xiao, Aiguo 1 Yang, Guoguo 1 Yin, Zhengwei 1 Zbinden, Christophe J. 1 Zhong, Juan all top 5 Cited in 21 Serials 6 Journal of Computational and Applied Mathematics 6 SIAM Journal on Scientific Computing 5 Journal of Computational Physics 4 BIT 3 Numerical Algorithms 3 Multiscale Modeling & Simulation 2 Advances in Difference Equations 1 Computers & Mathematics with Applications 1 Mathematics and Computers in Simulation 1 SIAM Journal on Numerical Analysis 1 Applied Numerical Mathematics 1 Numerical Methods for Partial Differential Equations 1 Journal of Scientific Computing 1 International Journal of Computer Mathematics 1 Computational and Applied Mathematics 1 Comptes Rendus. Mathématique. Académie des Sciences, Paris 1 Mathematical Biosciences and Engineering 1 SIAM Journal on Imaging Sciences 1 Journal of Numerical Mathematics and Stochastics 1 Stochastic and Partial Differential Equations. Analysis and Computations 1 SIAM/ASA Journal on Uncertainty Quantification all top 5 Cited in 14 Fields 41 Numerical analysis (65-XX) 30 Probability theory and stochastic processes (60-XX) 9 Ordinary differential equations (34-XX) 4 Partial differential equations (35-XX) 4 Biology and other natural sciences (92-XX) 2 Dynamical systems and ergodic theory (37-XX) 1 Integral equations (45-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Statistics (62-XX) 1 Computer science (68-XX) 1 Quantum theory (81-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Operations research, mathematical programming (90-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) Citations by Year