Applied and Computational Mathematics

Volume 4, Issue 2, April 2015

  • 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: Feb. 11, 2015
    Accepted: Feb. 26, 2015
    Published: Mar. 04, 2015
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    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... Show More
  • 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: Dec. 22, 2014
    Accepted: Feb. 06, 2015
    Published: Mar. 06, 2015
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    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 ... Show More
  • 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: Feb. 19, 2015
    Accepted: Mar. 09, 2015
    Published: Mar. 19, 2015
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    Abstract: In this note we study a new nn matrix of the form A=[a^(min⁡(i,j)-1) ]_(i,j=1)^n, where a1 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... Show More
  • 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: Feb. 25, 2015
    Accepted: Mar. 13, 2015
    Published: Mar. 21, 2015
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    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... Show More
  • A Galerkin Finite Element Method for Two-Point Boundary Value Problems of Ordinary Differential Equations

    Gentian Zavalani

    Issue: Volume 4, Issue 2, April 2015
    Pages: 64-68
    Received: Feb. 26, 2015
    Accepted: Mar. 16, 2015
    Published: Mar. 21, 2015
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    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 ... Show More
  • Transformation of Nonlinear Mixture Chopped Stochastic Program Model

    Togi Panjaitan, Iryanto Iryanto

    Issue: Volume 4, Issue 2, April 2015
    Pages: 69-76
    Received: Feb. 02, 2015
    Accepted: Mar. 03, 2015
    Published: Mar. 30, 2015
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    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 ... Show More
  • On Fractional Order Influenza A Epidemic Model

    Bonyah Ebenezer

    Issue: Volume 4, Issue 2, April 2015
    Pages: 77-82
    Received: Mar. 09, 2015
    Accepted: Mar. 24, 2015
    Published: Mar. 30, 2015
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    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... Show More