Diagonally drift-implicit Runge-Kutta methods of weak order one and two for Itô SDEs and stability analysis

DOI10.1016/j.apnum.2008.03.011zbMath1166.65304arXiv1303.5104OpenAlexW2095240846MaRDI QIDQ1007381

Kristian Debrabant, Andreas Rößler

Publication date: 20 March 2009

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1303.5104

zbMATH Keywords

stochastic differential equationasymptotic stabilityweak approximationimplicit methodmean-square stabilitystochastic Runge-Kutta method

Mathematics Subject Classification ID

Probabilistic models, generic numerical methods in probability and statistics (65C20) Stability and convergence of numerical methods for ordinary differential equations (65L20) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Numerical solutions to stochastic differential and integral equations (65C30)

Related Items (18)

Linear mean-square stability properties of semi-implicit weak order 2.0 Taylor schemes for systems of stochastic differential equations ⋮ THE NUMERICAL STABILITY OF STOCHASTIC ORDINARY DIFFERENTIAL EQUATIONS WITH ADDITIVE NOISE ⋮ Second-order balanced stochastic Runge-Kutta methods with multi-dimensional studies ⋮ A Micro-Macro Acceleration Method for the Monte Carlo Simulation of Stochastic Differential Equations ⋮ Weak second order S-ROCK methods for Stratonovich stochastic differential equations ⋮ A structural analysis of asymptotic mean-square stability for multi-dimensional linear stochastic differential systems ⋮ Mean-square \(A\)-stable diagonally drift-implicit integrators of weak second order for stiff Itô stochastic differential equations ⋮ A Runge-Kutta method for index 1 stochastic differential-algebraic equations with scalar noise ⋮ Runge-Kutta methods for third order weak approximation of SDEs with multidimensional additive noise ⋮ A class of weak second order split-drift stochastic Runge-Kutta schemes for stiff SDE systems ⋮ Study of micro-macro acceleration schemes for linear slow-fast stochastic differential equations with additive noise ⋮ Analysis of asymptotic mean-square stability of a class of Runge-Kutta schemes for linear systems of stochastic differential equations ⋮ Stability analysis and classification of Runge-Kutta methods for index 1 stochastic differential-algebraic equations with scalar noise ⋮ Truncated Milstein method for non-autonomous stochastic differential equations and its modification ⋮ Stochastic Runge-Kutta Rosenbrock type methods for SDE systems ⋮ On the stability of some second order numerical methods for weak approximation of Itô SDEs ⋮ New explicit stabilized stochastic Runge-Kutta methods with weak second order for stiff Itô stochastic differential equations ⋮ A-stable Runge-Kutta methods for stiff stochastic differential equations with multiplicative noise

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