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

Bakan, Hacer Oz
Yilmaz, Fikriye
Weber, Gerhard Wilhelm
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.


BENNER, Peter; Yücel, Hamdullah (2017-01-01)
We investigate an a posteriori error analysis of adaptive finite element approximations of linear-quadratic boundary optimal control problems under bilateral box constraints, which act on a Neumann boundary control. We use a symmetric interior Galerkin method as discretization technique. An efficient and reliable residual-type error estimator is introduced by invoking data oscillations. We then derive local upper and lower a posteriori error estimates for the boundary control problem. Adaptive mesh refineme...
Adaptive Symmetric Interior Penalty Galerkin (SIPG) method for optimal control of convection diffusion equations with control constraints
Yücel, Hamdullah; Karasözen, Bülent (2014-01-02)
In this paper, we study a posteriori error estimates of the upwind symmetric interior penalty Galerkin (SIPG) method for the control constrained optimal control problems governed by linear diffusion-convection-reaction partial differential equations. Residual based error estimators are used for the state, the adjoint and the control. An adaptive mesh refinement indicated by a posteriori error estimates is applied. Numerical examples are presented for convection dominated problems to illustrate the theoretic...
Analysis of a projection-based variational multiscale method for a linearly extrapolated BDF2 time discretization of the Navier-Stokes equations
Vargün, Duygu; Kaya Merdan, Songül; Department of Mathematics (2018)
This thesis studies a projection-based variational multiscale (VMS) method based on a linearly extrapolated second order backward difference formula (BDF2) to simulate the incompressible time-dependent Navier-Stokes equations (NSE). The method concerns adding stabilization based on projection acting only on the small scales. To give a basic notion of the projection-based VMS method, a three-scale VMS method is explained. Also, the principles of the projection-based VMS stabilization are provided. By using t...
Approximate l-state solutions of the D-dimensional Schrodinger equation for Manning-Rosen potential
IKHDAİR, SAMEER; Sever, Ramazan (Wiley, 2008-11-01)
The Schrodinger equation in D-dimensions for the Manning-Rosen potential with the centrifugal term is solved approximately to obtain bound states eigensolutions (eigenvalues and eigenfunctions). The Nikiforov-Uvarov (NU) method is used in the calculations. We present numerical calculations of energy eigenvalues to two- and four-dimensional systems for arbitrary quantum numbers n and 1, with three different values of the potential parameter alpha. It is shown that because of the interdimensional degeneracy o...
Approximate solution to the time-dependent Kratzer plus screened Coulomb potential in the Feinberg-Horodecki equation
Farout, Mahmoud; Sever, Ramazan; Ikhdair, Sameer M. (IOP Publishing, 2020-06-01)
We obtain the quantized momentum eigenvalues P-n together with space-like coherent eigenstates for the space-like counterpart of the Schrodinger equation, the Feinberg-Horodecki equation, with a combined Kratzer potential plus screened coulomb potential which is constructed by temporal counterpart of the spatial form of these potentials. The present work is illustrated with two special cases of the general form: the time-dependent modified Kratzer potential and the time-dependent screened Coulomb potential.
Citation Formats
H. O. Bakan, F. Yilmaz, and G. W. Weber, “Minimal truncation error constants for Runge-Kutta method for stochastic optimal control problems,” JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, pp. 196–207, 2018, Accessed: 00, 2020. [Online]. Available: