B-series for SDEs with application to exponential integrators for non-autonomous semi-linear problems

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Numerical solutions to stochastic differential and integral equations (65C30)

Cites Work

On post-Lie algebras, Lie-Butcher series and moving frames
Energy-preserving integrators and the structure of B-series
Composition of stochastic B-series with applications to implicit Taylor methods
B-series analysis of iterated Taylor methods
Rooted tree analysis of the order conditions of row-type scheme for stochastic differential equations
Multistep-multistage-multiderivative methods for ordinary differential equations
Multi-colored rooted tree analysis of the weak order conditions of a stochastic Runge-Kutta family
Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations
General order conditions for stochastic partitioned Runge-Kutta methods
Lie-Butcher theory for Runge-Kutta methods
Stochastic B-series and order conditions for exponential integrators
Runge-Kutta Lawson schemes for stochastic differential equations
A new class of structure-preserving stochastic exponential Runge-Kutta integrators for stochastic differential equations
A class of new Magnus-type methods for semi-linear non-commutative Itô stochastic differential equations
Order Conditions of Stochastic Runge--Kutta Methods by B-Series
Geometric Numerical Integration
Stochastic Taylor Expansions for the Expectation of Functionals of Diffusion Processes
Rooted Tree Analysis for Order Conditions of Stochastic Runge-Kutta Methods for the Weak Approximation of Stochastic Differential Equations
Numerical Methods for Stochastic Systems Preserving Symplectic Structure
B–Series Analysis of Stochastic Runge–Kutta Methods That Use an Iterative Scheme to Compute Their Internal Stage Values
Order conditions for commutator-free Lie group methods
B-series and Order Conditions for Exponential Integrators
Coefficients for the study of Runge-Kutta integration processes
Explicit Exponential Runge--Kutta Methods for Semilinear Parabolic Problems
Implicit Taylor methods for stiff stochastic differential equations
High strong order explicit Runge-Kutta methods for stochastic ordinary differential equations
Aromatic Butcher series
Stochastic differential equations. An introduction with applications.
Formulae for Mixed Moments of Wiener Processes and a Stochastic Area Integral

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