The numerical analysis of ordinary differential equations: Runge-Kutta and general linear methods
The numerical analysis of ordinary differential equations: Runge-Kutta and general linear methods
Stochastic differential equations (3rd ed.): an introduction with applications
Stochastic differential equations (3rd ed.): an introduction with applications
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Random generation of stochastic area integrals
SIAM Journal on Applied Mathematics
Equilibrium states of Runge Kutta schemes
ACM Transactions on Mathematical Software (TOMS)
The essential stability of local error control for dynamical systems
SIAM Journal on Numerical Analysis
High strong order explicit Runge-Kutta methods for stochastic ordinary differential equations
Applied Numerical Mathematics - Special issue celebrating the centenary of Runge-Kutta methods
Variable step size control in the numerical solution of stochastic differential equations
SIAM Journal on Applied Mathematics
Proceedings of the second world congress on Nonlinear analysts : part 2: part 2
Step size control in the numerical solution of stochastic differential equations
Journal of Computational and Applied Mathematics
Optimal approximation of stochastic differential equations by adaptive step-size control
Mathematics of Computation
Numerical solutions of stochastic differential equations — implementation and stability issues
Journal of Computational and Applied Mathematics - Special issue on numerical anaylsis 2000 Vol. VI: Ordinary differential equations and integral equations
Adaptive schemes for the numerical solution of SDEs: a comparison
Journal of Computational and Applied Mathematics
Mean-square stability properties of an adaptive time-stepping SDE solver
Journal of Computational and Applied Mathematics
SDELab: A package for solving stochastic differential equations in MATLAB
Journal of Computational and Applied Mathematics
A new adaptive Runge-Kutta method for stochastic differential equations
Journal of Computational and Applied Mathematics
On mean-square stability properties of a new adaptive stochastic Runge-Kutta method
Journal of Computational and Applied Mathematics
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We introduce a variable timestepping procedure using local error control for the pathwise (strong) numerical integration of a system of stochastic differential equations forced by a single Wiener process. The Milstein method is used to advance the numerical solution and the stepsizes are determined via two local error estimates that roughly correspond to leading order deterministic and stochastic local error components. One advantage of using two error controls is an increased flexibility that allows for the treatment of both drift and diffusion dominated regimes in a consistent manner. Numerical results are presented and the generalization of this approach to wider classes of problems and methods is discussed.