Families of efficient second order Runge-Kutta methods for the weak approximation of Itô stochastic differential equations

Abstract

Recently, a new class of second order Runge-Kutta methods for Itô stochastic differential equations with a multidimensional Wiener process was introduced by Rößler. In contrast to second order methods earlier proposed by other authors, this class has the advantage that the number of function evaluations depends only linearly on the number of Wiener processes and not quadratically. In this paper, we give a full classification of the coefficients of all explicit methods with minimal stage number. Based on this classification, we calculate the coefficients of an extension with minimized error constant of the well-known RK32 method to the stochastic case. For three examples, this method is compared numerically with known order two methods and yields very promising results.

arXiv admin note: substantial text overlap with arXiv:1303.4510

References in corpus (3)

• Rooted Tree Analysis for Order Conditions of Stochastic Runge-Kutta Methods for the Weak Approximation of Stochastic Differential Equations
• Classification of Stochastic Runge-Kutta Methods for the Weak Approximation of Stochastic Differential Equations
• Families of efficient second order Runge-Kutta methods for the weak approximation of Itô stochastic differential equations

Cited by in corpus (5)

• Families of efficient second order Runge-Kutta methods for the weak approximation of Itô stochastic differential equations
• Diagonally drift-implicit Runge-Kutta methods of weak order one and two for Itô SDEs and stability analysis
• A micro-macro acceleration method for the Monte Carlo simulation of stochastic differential equations
• Qualitative properties of numerical methods for the inhomogeneous geometric Brownian motion
• A Monte Carlo Method for 3D Radiative Transfer Equations with Multifractional Singular Kernels