References
- A. Abdulle and S. Cirilli, S-ROCK: Chebyshev methods for stiff stochastic differential equations, SIAM J. Sci. Comput. 30 (2008), pp. 997–1014.
- A. Abdulle and T. Li, S-ROCK methods for stiff Itô SDEs, Commun. Math. Sci. 6 (2008), pp. 845–868.
- J. Alcock and K. Burrage, A note on the balanced method, BIT Numer. Math. 46 (2006), pp. 689–710.
- S. Amiri and S.M. Hosseini, A class of balanced stochastic Runge-Kutta methods for stiff SDE systems, Numer. Algorithms 69 (2015), pp. 531–552.
- K. Burrage and T. Tian, Implicit stochastic Runge-Kutta methods for stochatic differential equations, BIT. Numer. Math. 44 (2004), pp. 21–39.
- M. Carletti, K. Burrage, and P.M. Burrage, Numerical simulation of stochastic ordinary differential equations in biomathematical modelling, Math. Comput. Simul. 64 (2004), pp. 271–277.
- D.T. Gillespie, Stochastic simulation of chemical kinetics, Annu. Rev. Phys. Chem. 58 (2007), pp. 35–55.
- A. Haghighi and S.M. Hosseini, A class of split-step balanced methods for stiff stochastic differential equations, Numer. Algorithms 61 (2012), pp. 141–162.
- A. Haghighi, S.M. Hosseini, and A. Rößler, Diagonally drift-implicit Runge-Kutta methods of strong order one for stiff stochastic differential systems, J. Comput. Appl. Math. 293 (2016), pp. 82–93.
- E. Hairer and G. Wanner, Solving Ordinary Differential Equations II. Stiff and Differential-Algebraic Problems, Springer, Berlin, 1996.
- C. Kahl and H. Schurz, Balanced Milstein methods for ordinary SDEs, Monte Carlo Methods Appl. 12 (2006), pp. 143–170.
- P.E. Kloeden and E. Platen, The Numerical Solution of Stochastic Differential Equations, Springer-Verlag, Berlin, 1992.
- Y. Komori and K. Burrage, Strong first order S-ROCK methods for stochastic differential equations, J. Comput. Appl. Math. 242 (2013), pp. 261–274.
- G.N. Milstein, Numerical Integration of Stochastic Differential Equations, Kluwer Academic, Dordrecht, 1995.
- G.N. Milstein, A theorem on the order of convergence of mean square approximations of solutions of systems of stochastic differential equations, Theory Probab. Appl. 32 (1988), pp. 738–741.
- G.N. Milstein, E. Platen, and H. Schurz, Balanced implicit methods for stiff stochastic systems, SIAM J. Numer. Anal. 35 (1998), pp. 1010–1019.
- G.N. Milstein and M.V. Tretyakov, Stochastic Numerics for Mathematical Physics, Springer, Berlin, 2004.
- A. Rößler, Runge-Kutta methods for the strong approximation of solutions of stochastic differential equations, SIAM J. Numer. Anal. 48 (2010), pp. 922–952.
- D.A. Vossa and A.Q.M. Khaliq, Split-step Adams–Moulton Milstein methods for systems of stiff stochastic differential equations, Int. J. Comput. Math. 92 (2015), pp. 995–1011.
- X. Wang, S. Gan, and D. Wang, A family of fully implicit Milstein methods for stiff stochastic differential equations with multiplicative noise, BIT. Numer. Math. 52 (2012), pp. 741–772.
- P. Wang and Z. Liu, Split-step backward balanced Milstein methods for stiff stochastic systems, Appl. Numer. Math. 59 (2009), pp. 1198–1213.
- M. Wiktorsson, Joint characteristic function and simultaneous simulation of iterated Itô integrals for multiple independent Brownian motions, Ann. Appl. Probab. 11 (2001), pp. 470–487.