\(A\)-stability of Runge-Kutta methods for systems with additive noise

DOI10.1007/BF01994846zbMath0755.65084OpenAlexW2069270950MaRDI QIDQ1195926

Diego Bricio Hernandez, Renato Spigler

Publication date: 26 January 1993

Published in: BIT (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01994846

zbMATH Keywords

stochastic differential equationsstochastic stabilityRunge-Kutta methods\(A\)-stabilityoptimal order of convergencestability regionsimplicit methodsNumerical stability

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Stochastic stability in control theory (93E15) 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) Probabilistic methods, stochastic differential equations (65C99)

Related Items

Preservation of probabilistic laws through Euler methods for ornstein-uhlenbeck process ⋮ Stabilized explicit methods for the approximation of stochastic systems driven by small additive noises ⋮ Stability in Distribution of Numerical Solutions for Stochastic Differential Equations ⋮ THE NUMERICAL STABILITY OF STOCHASTIC ORDINARY DIFFERENTIAL EQUATIONS WITH ADDITIVE NOISE ⋮ Basic Concepts of Numerical Analysis of Stochastic Differential Equations Explained by Balanced Implicit Theta Methods ⋮ Analytical and numerical investigation of stochastic differential equations with applications using an exponential Euler-Maruyama approach ⋮ Convergence rate of strong local linearization schemes for stochastic differential equations with additive noise ⋮ High order local linearization methods: an approach for constructing A-stable explicit schemes for stochastic differential equations with additive noise ⋮ Study of micro-macro acceleration schemes for linear slow-fast stochastic differential equations with additive noise ⋮ Asymptotical mean square stability of an equilibrium point of some linear numerical solutions with multiplicative noise ⋮ Higher-order semi-implicit Taylor schemes for Itô stochastic differential equations ⋮ STRONG PREDICTOR–CORRECTOR EULER METHODS FOR STOCHASTIC DIFFERENTIAL EQUATIONS ⋮ Convergence and asymptotic stability of the explicit Steklov method for stochastic differential equations ⋮ Almost sure asymptotic stability and convergence of stochastic Theta methods applied to systems of linear SDEs in ⋮ Mean-square stability of second-order Runge-Kutta methods for stochastic differential equations ⋮ On the numerical stability of simulation methods for SDEs under multiplicative noise in finance ⋮ Runge-Kutta methods for numerical solution of stochastic differential equations ⋮ A-stable Runge-Kutta methods for stiff stochastic differential equations with multiplicative noise ⋮ A high-order discontinuous Galerkin method for Itô stochastic ordinary differential equations ⋮ Diagonally drift-implicit Runge-Kutta methods of weak order one and two for Itô SDEs and stability analysis ⋮ Characterization of bistability for stochastic multistep methods ⋮ Convergence and stability of implicit Runge-Kutta methods for systems with multiplicative noise

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Discretization and simulation of stochastic differential equations
• Simulation studies on time discrete diffusion approximations
• Continuous Markov processes and stochastic equations
• On the Efficient Implementation of Implicit Runge-Kutta Methods
• Stratonovich and Ito Stochastic Taylor Expansions
• Numerical Solution of Stochastic Differential Equations with Constant Diffusion Coefficients
• Numerical Treatment of Stochastic Differential Equations
• On the implementation of implicit Runge-Kutta methods
• A special stability problem for linear multistep methods