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, cilt.331, ss.196-207, 2018 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 331
  • Basım Tarihi: 2018
  • Doi Numarası: 10.1016/j.cam.2017.10.011
  • Dergi Adı: JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.196-207
  • Anahtar Kelimeler: Optimal control, Runge-Kutta method, Stochastic differential equation, Stratonovich-Taylor expansion, Numerical solution, Minimal truncation error, DIFFERENTIAL-EQUATIONS, ORDER CONDITIONS, APPROXIMATION
  • Gazi Üniversitesi Adresli: Evet

Özet

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.