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

DOI10.1080/00207160.2014.915963zbMath1316.60100OpenAlexW1984965123MaRDI QIDQ5248080

David A. Voss, Abdul Q. M. Khaliq

Publication date: 27 April 2015

Published in: International Journal of Computer Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00207160.2014.915963

zbMATH Keywords

stochastic differential equationspredictor-corrector methodstiff equationssplit-step methodmean-square stability

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Stability and convergence of numerical methods for ordinary differential equations (65L20) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Numerical solutions to stochastic differential and integral equations (65C30)

Related Items (13)

Split-step double balanced approximation methods for stiff stochastic differential equations ⋮ Improving split-step forward methods by ODE solver for stiff stochastic differential equations ⋮ Solving the stochastic differential systems with modified split-step Euler-Maruyama method ⋮ Modified stochastic theta methods by ODEs solvers for stochastic differential equations ⋮ Mean-square stability of split-step theta Milstein methods for stochastic differential equations ⋮ Split-step Milstein methods for multi-channel stiff stochastic differential systems ⋮ Stability of the drift-implicit and double-implicit Milstein schemes for nonlinear SDEs ⋮ Stability analysis of split-step \(\theta \)-Milstein method for a class of \(n\)-dimensional stochastic differential equations ⋮ Improved Euler-Maruyama method for numerical solution of the Itô stochastic differential systems by composite previous-current-step idea ⋮ Convergence, non-negativity and stability of a new lobatto IIIC-Milstein method for a pricing option approach based on stochastic volatility model ⋮ Unnamed Item ⋮ Convergence and stability of split-step theta methods with variable step-size for stochastic pantograph differential equations ⋮ Study on split-step Rosenbrock type method for stiff stochastic differential systems

Cites Work

• A class of split-step balanced methods for stiff stochastic differential equations
• Convergence and stability of the split-step \(\theta \)-method for stochastic differential equations
• Split-step backward balanced Milstein methods for stiff stochastic systems
• The improved split-step θ methods for stochastic differential equation
• Efficient Split Linear Multistep Methods for Stiff Ordinary Differential Equations
• Strong Convergence of Euler-Type Methods for Nonlinear Stochastic Differential Equations
• Five-stage Milstein methods for SDEs
• Stability Analysis of Numerical Schemes for Stochastic Differential Equations
• Balanced Milstein Methods for Ordinary SDEs
• The composite Euler method for stiff stochastic differential equations
• Implicit Taylor methods for stiff stochastic differential equations

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