Journal of Computational and Applied Mathematics
Numerical simulation of a linear stochastic oscillator with additive noise
Applied Numerical Mathematics
Mean-square stability of second-order Runge-Kutta methods for stochastic differential equations
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
Numerical solution of stochastic differential problems in the biosciences
Journal of Computational and Applied Mathematics - Special issue: International workshop on the technological aspects of mathematics
Mean-square stability properties of an adaptive time-stepping SDE solver
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
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
Applied Numerical Mathematics
Interlaced Euler scheme for stiff systems of stochastic differential equations
Proceedings of the 2009 ACM symposium on Applied Computing
Journal of Computational and Applied Mathematics
The fully implicit stochastic-α method for stiff stochastic differential equations
Journal of Computational Physics
Split-step forward methods for stochastic differential equations
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
Mean-square stability of second-order Runge-Kutta methods for stochastic differential equations
Journal of Computational and Applied Mathematics
Numerical solution of stochastic differential problems in the biosciences
Journal of Computational and Applied Mathematics - Special issue: International workshop on the technological aspects of mathematics
Compensated stochastic theta methods for stochastic differential equations with jumps
Applied Numerical Mathematics
Convergence and stability of the split-step θ-method for stochastic differential equations
Computers & Mathematics with Applications
Journal of Computational and Applied Mathematics
The composite Milstein methods for the numerical solution of Ito stochastic differential equations
Journal of Computational and Applied Mathematics
Mathematics and Computers in Simulation
SIAM Journal on Numerical Analysis
Higher-order semi-implicit Taylor schemes for Itô stochastic differential equations
Journal of Computational and Applied Mathematics
Mean-square stability analysis of numerical schemes for stochastic differential systems
Journal of Computational and Applied Mathematics
Weak second order S-ROCK methods for Stratonovich stochastic differential equations
Journal of Computational and Applied Mathematics
Applied Numerical Mathematics
Delay-dependent stability analysis of numerical methods for stochastic delay differential equations
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
Stochastic Evolution Equations in Portfolio Credit Modelling
SIAM Journal on Financial Mathematics
Computers & Mathematics with Applications
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
Asymptotic stability of balanced methods for stochastic jump-diffusion differential equations
Journal of Computational and Applied Mathematics
A stochastic model for prevention and control of HIV/AIDS transmission dynamics
LSMS'07 Proceedings of the 2007 international conference on Life System Modeling and Simulation
Asymptotic moment boundedness of the numerical solutions of stochastic differential equations
Journal of Computational and Applied Mathematics
A derivative-free explicit method with order 1.0 for solving stochastic delay differential equations
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
Asymptotic mean-square stability of two-step Maruyama schemes for stochastic differential equations
Journal of Computational and Applied Mathematics
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Stability analysis of numerical methods for ordinary differential equations (ODEs) is motivated by the question "for what choices of stepsize does the numerical method reproduce the characteristics of the test equation?" We study a linear test equation with a multiplicative noise term, and consider mean-square and asymptotic stability of a stochastic version of the theta method. We extend some mean-square stability results in [Saito and Mitsui, SIAM. J. Numer. Anal., 33 (1996), pp. 2254--2267]. In particular, we show that an extension of the deterministic A-stability property holds. We also plot mean-square stability regions for the case where the test equation has real parameters. For asymptotic stability, we show that the issue reduces to finding the expected value of a parametrized random variable. We combine analytical and numerical techniques to get insights into the stability properties. For a variant of the method that has been proposed in the literature we obtain precise analytic expressions for the asymptotic stability region. This allows us to prove a number of results. The technique introduced is widely applicable, and we use it to show that a fully implicit method suggested by [Kloeden and Platen, Numerical Solution of Stochastic Differential Equations, Springer-Verlag, 1992] has an asymptotic stability extension of the deterministic A-stability property. We also use the approach to explain some numerical results reported in [Milstein, Platen, and Schurz, SIAM J. Numer. Anal., 35 (1998), pp. 1010--1019.]