Numerical solutions of stochastic differential equations – implementation and stability issues
Copyright policy )Numerical solutions of stochastic differential equations – implementation and stability issues
The first part of this paper reviews known definitions of various types of stability associated with exact solutions of stochastic differential equations (SDEs) and with numerical solutions of SDEs. After briefly commenting on the implementation of numerical methods involving fixed stepsize, a variable stepsize stochastic Runge-Kutta method is presented and its implementation is discussed. The effectiveness of this method is demonstrated for a Stratonovich SDE example by comparing error and steps needed when variable stepsize is used and when fixed stepsize is used.
- Nagoya University Japan
- Queensland University of Technology Australia
- University of Queensland Australia
- University of Queensland Australia
- University of Queensland Australia
Ordinary differential equations and systems with randomness, error bound, Runge-kutta Methods, Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations, 780101 Mathematical sciences, C1, Mesh generation, refinement, and adaptive methods for ordinary differential equations, Stratonovich equation, Error bounds for numerical methods for ordinary differential equations, Numerical solutions to stochastic differential and integral equations, Variable Stepsize, Applied Mathematics, Systems, Variable stepsize, stability, stochastic differential equations, Stochastic ordinary differential equations (aspects of stochastic analysis), Stochastic Differential Equations, Computational Mathematics, variable stepsize implementation techniques, Applied, Stochastic differential equations, Order Conditions, 230116 Numerical Analysis, variable stepsize stochastic Runge-Kutta method, Stability, Mathematics
Ordinary differential equations and systems with randomness, error bound, Runge-kutta Methods, Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations, 780101 Mathematical sciences, C1, Mesh generation, refinement, and adaptive methods for ordinary differential equations, Stratonovich equation, Error bounds for numerical methods for ordinary differential equations, Numerical solutions to stochastic differential and integral equations, Variable Stepsize, Applied Mathematics, Systems, Variable stepsize, stability, stochastic differential equations, Stochastic ordinary differential equations (aspects of stochastic analysis), Stochastic Differential Equations, Computational Mathematics, variable stepsize implementation techniques, Applied, Stochastic differential equations, Order Conditions, 230116 Numerical Analysis, variable stepsize stochastic Runge-Kutta method, Stability, Mathematics
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