Solving optimal control problems of Fredholm constraint optimality via the reproducing kernel Hilbert space method with error estimates and convergence analysis

2019 ◽  
Author(s):  
Omar Abu Arqub ◽  
Nabil Shawagfeh
Keyword(s):  
Optimal Control ◽  
Hilbert Space ◽  
Convergence Analysis ◽  
Error Estimates ◽  
Reproducing Kernel ◽  
Optimal Control Problems ◽  
Reproducing Kernel Hilbert Space ◽  
Control Problems ◽  
Space Method

scholarly journals PICARD-REPRODUCING KERNEL HILBERT SPACE METHOD FOR SOLVING GENERALIZED SINGULAR NONLINEAR LANE-EMDEN TYPE EQUATIONS

2015 ◽  
Vol 20 (6) ◽  
pp. 754-767 ◽  
Author(s):  
Babak Azarnavid ◽  
Foroud Parvaneh ◽  
Saeid Abbasbandy
Keyword(s):  
Hilbert Space ◽  
Iterative Method ◽  
Error Estimates ◽  
Reproducing Kernel ◽  
Reproducing Kernel Hilbert Space ◽  
Picard Iteration ◽  
Combined Method ◽  
Numerical Examples ◽  
Space Method ◽  
Good Agreement

An iterative method is discussed with respect to its effectiveness and capability of solving singular nonlinear Lane-Emden type equations using reproducing kernel Hilbert space method combined with the Picard iteration. Some new error estimates for application of the method are established. We prove the convergence of the combined method. The numerical examples demonstrates a good agreement between numerical results and analytical predictions.

Error Estimates of Mixed Methods for Optimal Control Problems Governed by General Elliptic Equations

2016 ◽  
Vol 8 (6) ◽  
pp. 1050-1071 ◽  
Author(s):  
Tianliang Hou ◽  
Li Li
Keyword(s):  
Optimal Control ◽  
Finite Element ◽  
Error Estimates ◽  
Elliptic Equations ◽  
Optimal Control Problems ◽  
Mixed Finite Element ◽  
Control Variable ◽  
The State ◽  
Control Problems ◽  
General Elliptic

AbstractIn this paper, we investigate the error estimates of mixed finite element methods for optimal control problems governed by general elliptic equations. The state and co-state are approximated by the lowest order Raviart-Thomas mixed finite element spaces and the control variable is approximated by piecewise constant functions. We derive L2 and H–1-error estimates both for the control variable and the state variables. Finally, a numerical example is given to demonstrate the theoretical results.

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