High order local linearization methods: an approach for constructing A-stable explicit schemes for stochastic differential equations with additive noise

DOI10.1007/s10543-010-0272-6zbMath1205.65027OpenAlexW1967726010MaRDI QIDQ1960209

H. de la Cruz Cancino, J. C. Jimenez, F. Carbonell, R. J. Biscay, Tohru Ozaki

Publication date: 13 October 2010

Published in: BIT (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10543-010-0272-6

zbMATH Keywords

convergencenumerical integrationWiener processstochastic differential equationsA-stabilityRunge-Kutta schemesadditive noiselocal linearization methodTaylor schemes

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Stability and convergence of numerical methods for ordinary differential equations (65L20) Ordinary differential equations and systems with randomness (34F05) Numerical methods for initial value problems involving ordinary differential equations (65L05) 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 (12)

Stabilized explicit methods for the approximation of stochastic systems driven by small additive noises ⋮ An explicit numerical scheme for the computer simulation of the stochastic transport equation ⋮ First-order weak balanced schemes for stochastic differential equations ⋮ Convergence rate of strong local linearization schemes for stochastic differential equations with additive noise ⋮ Study of micro-macro acceleration schemes for linear slow-fast stochastic differential equations with additive noise ⋮ On the numerical integration of the undamped harmonic oscillator driven by independent additive Gaussian white noises ⋮ Asymptotic moment boundedness of the numerical solutions of stochastic differential equations ⋮ Convergence rate of weak local linearization schemes for stochastic differential equations with additive noise ⋮ A stochastic exponential Euler scheme for simulation of stiff biochemical reaction systems ⋮ Locally linearized methods for the simulation of stochastic oscillators driven by random forces ⋮ Asymptotically optimal approximation of some stochastic integrals and its applications to the strong second-order methods ⋮ A-stable Runge-Kutta methods for stiff stochastic differential equations with multiplicative noise

Uses Software

• Expokit
• RODAS

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