Minimal truncation error constants for Runge-Kutta method for stochastic optimal control problems

Bakan H. O., YILMAZ F. N., Weber G.

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, vol.331, pp.196-207, 2018 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 331
  • Publication Date: 2018
  • Doi Number: 10.1016/j.cam.2017.10.011
  • Journal Name: JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.196-207
  • Keywords: Optimal control, Runge-Kutta method, Stochastic differential equation, Stratonovich-Taylor expansion, Numerical solution, Minimal truncation error, DIFFERENTIAL-EQUATIONS, ORDER CONDITIONS, APPROXIMATION
  • Gazi University Affiliated: Yes

Abstract

In this work, we obtain strong order-1 conditions with minimal truncation error constants of Runge-Kutta method for the optimal control of stochastic differential equations (SDEs). We match Stratonovich-Taylor expansion of the exact solution with Stratonovich-Taylor expansion of our approximation method that is defined by the Runge-Kutta scheme, term by term, in order to get the strong order-1 conditions. By a conclusion and an outlook to future research, the paper ends. (C) 2017 Elsevier B.V. All rights reserved.