Stability analysis of explicit and implicit stochastic Runge-Kutta methods for stochastic differential equations

Stochastic Runge-Kutta Software Package for Stochastic Differential Equations

M. N. Gevorkyan,1, * T. R. Velieva,1, † A. V. Korolkova,1, ‡ D. S. Kulyabov,1, 2, S and L. A. Sevastyanov1, 3, ¶ Department of Applied Probability and Informatics Peoples’ Friendship University of Russia Miklukho-Maklaya str. 6, Moscow, 117198, Russia Laboratory of Information Technologies Joint Institute for Nuclear Research Joliot-Curie 6, Dubna, Moscow region, 141980, Russia Bogoliubov Labor...

Supplement: Efficient weak second order stochastic Runge-Kutta methods for non-commutative Stratonovich stochastic differential equations

This paper gives a modification of a class of stochastic Runge-Kutta methods proposed in a paper by Komori (2007). The slight modification can reduce the computational costs of the methods significantly.

Validated Explicit and Implicit Runge-Kutta Methods∗†

A set of validated numerical integration methods based on explicit and implicit Runge-Kutta schemes is presented to solve, in a guaranteed way, initial value problems of ordinary differential equations. Runge-Kutta methods are well-known to have strong stability properties, which make them appealing to be the basis of validated numerical integration methods. A new approach to bound the local tr...

Implicit Runge-Kutta Methods for Lipschitz Continuous Ordinary Differential Equations

Implicit Runge-Kutta(IRK) methods for solving the nonsmooth ordinary differential equation (ODE) involve a system of nonsmooth equations. We show superlinear convergence of the slanting Newton method for solving the system of nonsmooth equations. We prove the slanting differentiability and give a slanting function for the involved function. We develop a new code based on the slanting Newton met...

Fast Communication Two-stage Stochastic Runge-kutta Methods for Stochastic Differential Equations with Jump Diffusion