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Numerical Solution of an Optimal Control Problem Governed by Two Dimensional Schrodinger Equation
Fatma Toyoglu,
Gabil Yagubov
Issue:
Volume 4, Issue 2, April 2015
Pages:
30-38
Received:
11 February 2015
Accepted:
26 February 2015
Published:
4 March 2015
Abstract: In this study, the finite difference method is applied to an optimal control problem controlled by two functions which are in the coefficients of two-dimensional Schrodinger equation. Convergence of the finite difference approximation according to the functional is proved. We have used the implicit method for solving the two-dimensional Schrodinger equation. Although the implicit scheme obtained from solution of the system of the linear equations is generally numerically stable and convergent without time-step condition, the solution of considered equation is numerically stable with time-step condition, due to the gradient term.
Abstract: In this study, the finite difference method is applied to an optimal control problem controlled by two functions which are in the coefficients of two-dimensional Schrodinger equation. Convergence of the finite difference approximation according to the functional is proved. We have used the implicit method for solving the two-dimensional Schrodinger...
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The Continuous Finite Element Methods for a Simple Case of Separable Hamiltonian Systems
Qiong Tang,
Luohua Liua,
Yujun Zheng
Issue:
Volume 4, Issue 2, April 2015
Pages:
39-46
Received:
22 December 2014
Accepted:
6 February 2015
Published:
6 March 2015
Abstract: Combined with the characteristics of separable Hamiltonian systems and the finite element methods of ordinary differential equations, we prove that the composition of linear, quadratic, cubic finite element methods are symplectic integrator to separable Hamiltonian systems, i.e. the symplectic condition is preserved exactly, but the energy is only approximately conservative after compound. These conclusions are confirmed by our numerical experiments.
Abstract: Combined with the characteristics of separable Hamiltonian systems and the finite element methods of ordinary differential equations, we prove that the composition of linear, quadratic, cubic finite element methods are symplectic integrator to separable Hamiltonian systems, i.e. the symplectic condition is preserved exactly, but the energy is only ...
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A Particular Matrix, Its Inversion and Some Norms
Seyyed Hossein Jafari-Petroudi,
Behzad Pirouz
Issue:
Volume 4, Issue 2, April 2015
Pages:
47-52
Received:
19 February 2015
Accepted:
9 March 2015
Published:
19 March 2015
Abstract: In this note we study a new nn matrix of the form A=[a^(min(i,j)-1) ]_(i,j=1)^n, where a1 is a real positive constant. We find determinant and inversion of this matrix and its Hadamard inverse. Then some bounds for the spectral norm of this matrix are presented. Finally we represent some properties of particular block diagonal matrices that their diagonal elements are these matrices.
Abstract: In this note we study a new nn matrix of the form A=[a^(min(i,j)-1) ]_(i,j=1)^n, where a1 is a real positive constant. We find determinant and inversion of this matrix and its Hadamard inverse. Then some bounds for the spectral norm of this matrix are presented. Finally we represent some properties of particular block diagonal matrices that thei...
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A Mathematical Model for the Dynamics of Cholera with Control Measures
Stephen Edward,
Nkuba Nyerere
Issue:
Volume 4, Issue 2, April 2015
Pages:
53-63
Received:
25 February 2015
Accepted:
13 March 2015
Published:
21 March 2015
Abstract: Cholera, an acute gastro-intestinal infection and a waterborne disease continues to emerge in developing countries and remains an important global health challenge. In this paper, we formulate a mathematical model that captures some essential dynamics of cholera transmission with public health educational campaigns, vaccination, sanitation and treatment as control strategies in limiting the disease. The reproduction numbers with single and combined controls are computed and compared with each other to assess the possible community benefits. Numerical simulation shows that in a unique control strategy, treatment yields the best results followed by education campaign, then sanitation and vaccination being the last. Furthermore, we noted that the control of cholera is very much better when we incorporated more than one strategy, in two controls the results were better than one strategy, and in three control strategies the results were far better than in two control strategies. Further simulations with all four interventions showed the best results among all combinations attained before. We performed sensitivity analysis on the key parameters that drive the disease dynamics in order to determine their relative importance to disease transmission and prevalence.
Abstract: Cholera, an acute gastro-intestinal infection and a waterborne disease continues to emerge in developing countries and remains an important global health challenge. In this paper, we formulate a mathematical model that captures some essential dynamics of cholera transmission with public health educational campaigns, vaccination, sanitation and trea...
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A Galerkin Finite Element Method for Two-Point Boundary Value Problems of Ordinary Differential Equations
Issue:
Volume 4, Issue 2, April 2015
Pages:
64-68
Received:
26 February 2015
Accepted:
16 March 2015
Published:
21 March 2015
Abstract: In this paper, we present a new method for solving two-point boundary value problem for certain ordinary differential equation. The two point boundary value problems have great importance in chemical engineering, deflection of beams etc. In this study, Galerkin finite element method is developed for inhomogeneous second-order ordinary differential equations. Several examples are solved to demonstrate the application of the finite element method. It is shown that the finite element method is simple, accurate and well behaved in the presence of singularities.
Abstract: In this paper, we present a new method for solving two-point boundary value problem for certain ordinary differential equation. The two point boundary value problems have great importance in chemical engineering, deflection of beams etc. In this study, Galerkin finite element method is developed for inhomogeneous second-order ordinary differential ...
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Transformation of Nonlinear Mixture Chopped Stochastic Program Model
Togi Panjaitan,
Iryanto Iryanto
Issue:
Volume 4, Issue 2, April 2015
Pages:
69-76
Received:
2 February 2015
Accepted:
3 March 2015
Published:
30 March 2015
Abstract: This paper describes a new approach to obtain the global optimization problem of nonlinear mixture chopped stochastic program model. The study focused on the issue of two-stage stochastic with the lack of nonlinearity, which is contained in the objective function and constraints. Variables in the first stage is worth a count, while the variable in the second stage is a mixture of chopped and continuous. Issues formulated by scenario-based representation. The approach used to complete the large scale nonlinear mix chopped program lifting unfounded variable value of the limit, forcing a variable-value basis chopped. Problems reduced is processed at the time of chopped variables held constant, and the changes made during discrete steps, in order to obtain a global optimal solution.
Abstract: This paper describes a new approach to obtain the global optimization problem of nonlinear mixture chopped stochastic program model. The study focused on the issue of two-stage stochastic with the lack of nonlinearity, which is contained in the objective function and constraints. Variables in the first stage is worth a count, while the variable in ...
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On Fractional Order Influenza A Epidemic Model
Issue:
Volume 4, Issue 2, April 2015
Pages:
77-82
Received:
9 March 2015
Accepted:
24 March 2015
Published:
30 March 2015
Abstract: This paper examines the fractional order of influenza using an epidemic model. The stability of disease-free and positive fixed points is explored and studied. The Adams-Bashforth-Moulton algorithm is employed to determine the solution and also simulate the system of differential equations. It is observed that Adams-Bashforth-Moulton method gives similar results as obtained in Runge-Kutta technique and ODE 45.
Abstract: This paper examines the fractional order of influenza using an epidemic model. The stability of disease-free and positive fixed points is explored and studied. The Adams-Bashforth-Moulton algorithm is employed to determine the solution and also simulate the system of differential equations. It is observed that Adams-Bashforth-Moulton method gives s...
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