Convergence Analysis of Discontinuous Finite Volume Methods for Elliptic Optimal Control Problems

2016 ◽  
Vol 13 (02) ◽  
pp. 1640012 ◽  
Author(s):  
Ruchi Sandilya ◽  
Sarvesh Kumar
Keyword(s):  
Order Of Convergence ◽  
Optimal Control Problems ◽  
Finite Volume Methods ◽  
Optimal Order ◽  
Control Problems ◽  
State Variables ◽  
Optimal Order Of Convergence ◽  
Piecewise Constant ◽  
Adjoint State ◽  
Variational Discretization

In this paper, we discuss the convergence analysis of discontinuous finite volume methods applied to distribute the optimal control problems governed by a class of second-order linear elliptic equations. In order to approximate the control, two different methodologies are adopted: one is the method of variational discretization and second is piecewise constant discretization technique. For variational discretization method, optimal order of convergence in the [Formula: see text]-norm for state, adjoint state and control variables is derived. Moreover, optimal order of convergence in discrete [Formula: see text]-norm is also derived for state and adjoint state variables. Whereas, for piecewise constant approximation of control, first order convergence is derived for control, state and adjoint state variables in the [Formula: see text]-norm. In addition to that, optimal order of convergence in discrete [Formula: see text]-norm is derived for state and adjoint state variables. Also, some numerical experiments are conducted to support the derived theoretical convergence rate.

scholarly journals Four-Point Optimal Sixteenth-Order Iterative Method for Solving Nonlinear Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Malik Zaka Ullah ◽  
A. S. Al-Fhaid ◽  
Fayyaz Ahmad
Keyword(s):  
Iterative Method ◽  
Nonlinear Equations ◽  
Numerical Experiments ◽  
Order Of Convergence ◽  
Iterative Scheme ◽  
Optimal Order ◽  
Optimal Order Of Convergence

We present an iterative method for solving nonlinear equations. The proposed iterative method has optimal order of convergence sixteen in the sense of Kung-Traub conjecture (Kung and Traub, 1974); it means that the iterative scheme uses five functional evaluations to achieve 16(=25-1) order of convergence. The proposed iterative method utilizes one derivative and four function evaluations. Numerical experiments are made to demonstrate the convergence and validation of the iterative method.

Research on a collocation approach and three metaheuristic techniques based on MVO, MFO, and WOA for optimal control of fractional differential equation

2021 ◽  
pp. 107754632110514
Author(s):  
Asiyeh Ebrahimzadeh ◽  
Raheleh Khanduzi ◽  
Samaneh P A Beik ◽  
Dumitru Baleanu
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Focal Point ◽  
Control Problems ◽  
Operational Matrices ◽  
State Variables ◽  
Caputo Fractional Derivatives ◽  
Fractional Optimal Control ◽  
Whale Optimization ◽  
Fractional Optimal Control Problems

Exploiting a comprehensive mathematical model for a class of systems governed by fractional optimal control problems is the significant focal point of the current paper. The efficiency index is a function of both control and state variables and the dynamic control system relies on Caputo fractional derivatives. The attributes of Bernoulli polynomials and their operational matrices of fractional Riemann–Liouville integrations are applied to convert the optimization problem to the nonlinear programing problem. Executing multi-verse optimizer, moth-flame optimization, and whale optimization algorithm terminate to the most excellent solution of fractional optimal control problems. A study on the advantage and performance between these approaches is analyzed by some examples. Comprehensive analysis ascertains that moth-flame optimization significantly solves the example. Furthermore, the privilege and advantage of preference with its accuracy are numerically indicated. Finally, results demonstrate that the objective function value gained by moth-flame optimization in comparison with other algorithms effectively decreased.

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