An Infinite Family of Second Order Weak Explicit Runge-Kutta Methods

Article type: Research Article

Authors: Vigo–Aguiar, J.^a | Tocino, A.^b

Affiliations: [a] Departamento de Matematica Aplicada, Universidad de Salamanca, E37008 Salamanca, Spain. E-mail: [email protected] | [b] Departamento de Matemáticas, Universidad de Salamanca, E37008 Salamanca, Spain. E-mail: [email protected]

Abstract: A quick overview of the fundamental concepts for the construction of weak methods for the numerical solution of stochastic differential equations and a new way to construct these methods are presented. As in the deterministic case, the presented procedure to obtain these methods consists in the comparison of their stochastic expansions with the corresponding Taylor scheme. In this way the authors construct a generalization of the classical second order two step explicit Runge-Kutta family of methods for ordinary differential equations. The obtained methods require the computation of a random variable at each step and avoid derivatives.

Keywords: Stochastic differential equations, weak approximation, Runge-Kutta methods, weak numerical schemes, explicit schemes

Keywords: 65U05, 60H10, 34F05

DOI: 10.3233/JCM-2001-1105

Journal: Journal of Computational Methods in Sciences and Engineering, vol. 1, no. 1, pp. 125-134, 2001