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International Journal of Computer Mathematics Volume 92, 2015 - Issue 5
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Section B

Split-step Adams–Moulton Milstein methods for systems of stiff stochastic differential equations

David A. VossDepartment of Mathematics, Western Illinois University, Macomb, IL61455, USACorrespondence[email protected]
&
Abdul Q. M. KhaliqDepartment of Mathematical Sciences and Center for Computational Science, Middle Tennessee State University, Murfreesboro, TN37132, USA
Pages 995-1011 | Received 22 Jan 2014, Accepted 10 Apr 2014, Published online: 22 May 2014

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K. Nouri, H. Ranjbar & L. Torkzadeh. (2020) Study on split-step Rosenbrock type method for stiff stochastic differential systems. International Journal of Computer Mathematics 97:4, pages 818-836.
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Amir Haghighi & Andreas Rößler. (2019) Split-step double balanced approximation methods for stiff stochastic differential equations. International Journal of Computer Mathematics 96:5, pages 1030-1047.
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Yu Xiao, Mahmoud A. Eissa & Boping Tian. (2018) Convergence and stability of split-step theta methods with variable step-size for stochastic pantograph differential equations. International Journal of Computer Mathematics 95:5, pages 939-960.
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Articles from other publishers (17)

Hassan Ranjbar, Leila Torkzadeh, Dumitru Baleanu & Kazem Nouri. (2023) Simulating systems of Itô SDEs with split-step $ (\alpha, \beta) $-Milstein scheme. AIMS Mathematics 8:2, pages 2576-2590.
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Leila Torkzadeh, Hassan Ranjbar, Sanda Micula & Kazem Nouri. (2022) Convergence and Stability of a Split-Step Exponential Scheme Based on the Milstein Methods. Symmetry 14:11, pages 2413.
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Hassan Ranjbar, Kazem Nouri & Leila Torkzadeh. (2022) Improvement of Split-Step Forward Milstein Schemes for SODEs Arising in Mathematical Physics. Mathematical Problems in Engineering 2022, pages 1-7.
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K. Nouri. (2021) Improving split-step forward methods by ODE solver for stiff stochastic differential equations. Mathematical Sciences 16:1, pages 51-57.
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Mourad S. Semary, M. T. M. Elbarawy & Aisha F. Fareed. (2022) Discrete Temimi-Ansari method for solving a class of stochastic nonlinear differential equations. AIMS Mathematics 7:4, pages 5093-5105.
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Kazem Nouri, Hassan Ranjbar, Dumitru Baleanu & Leila Torkzadeh. (2021) Investigation on Ginzburg-Landau equation via a tested approach to benchmark stochastic Davis-Skodje system. Alexandria Engineering Journal 60:6, pages 5521-5526.
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Mahmoud A. Eissa & Qiang Ye. (2020) Convergence, non-negativity and stability of a new Lobatto IIIC-Milstein method for a pricing option approach based on stochastic volatility model. Japan Journal of Industrial and Applied Mathematics 38:2, pages 391-424.
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Hao Zhu, Mulan Wang, Kun Liu & Weiye Xu. (2021) NURBS Modeling and Curve Interpolation Optimization of 3D Graphics. Computers, Materials & Continua 66:2, pages 1799-1811.
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Kazem Nouri, Hassan Ranjbar & Leila Torkzadeh. (2020) The explicit approximation approach to solve stiff chemical Langevin equations. The European Physical Journal Plus 135:9.
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Kazem Nouri, Hassan Ranjbar & Leila Torkzadeh. (2020) Solving the stochastic differential systems with modified split-step Euler-Maruyama method. Communications in Nonlinear Science and Numerical Simulation 84, pages 105153.
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D. Ahmadian, O. Farkhondeh Rouz & L.V. Ballestra. (2019) Stability analysis of split-step θ-Milstein method for a class of n-dimensional stochastic differential equations. Applied Mathematics and Computation 348, pages 413-424.
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Kazem Nouri, Hassan Ranjbar & Leila Torkzadeh. (2019) Modified stochastic theta methods by ODEs solvers for stochastic differential equations. Communications in Nonlinear Science and Numerical Simulation 68, pages 336-346.
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Jinran Yao & Siqing Gan. (2018) Stability of the drift-implicit and double-implicit Milstein schemes for nonlinear SDEs. Applied Mathematics and Computation 339, pages 294-301.
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Kazem Nouri, Hassan Ranjbar & Leila Torkzadeh. (2018) Improved Euler–Maruyama Method for Numerical Solution of the Itô Stochastic Differential Systems by Composite Previous-Current-Step Idea. Mediterranean Journal of Mathematics 15:3.
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Mahmoud A. Eissa, Haiying Zhang & Yu Xiao. (2018) Mean-Square Stability of Split-Step Theta Milstein Methods for Stochastic Differential Equations. Mathematical Problems in Engineering 2018, pages 1-13.
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Mahmoud Eissa & Boping Tian. (2017) Lobatto-Milstein Numerical Method in Application of Uncertainty Investment of Solar Power Projects. Energies 10:1, pages 43.
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V. Reshniak, A.Q.M. Khaliq, D.A. Voss & G. Zhang. (2015) Split-step Milstein methods for multi-channel stiff stochastic differential systems. Applied Numerical Mathematics 89, pages 1-23.
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