Applied and Computational Mathematics

Volume 5, Issue 2, April 2016

  • A Highly Accurate Approximation of Conic Sections by Quartic Bézier Curves

    Zhi Liu, Na Wei, Jieqing Tan, Xiaoyan Liu

    Issue: Volume 5, Issue 2, April 2016
    Pages: 40-45
    Received: Feb. 18, 2016
    Accepted: Feb. 26, 2016
    Published: Mar. 09, 2016
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    Abstract: A new approximation method for conic section by quartic Bézier curves is proposed. This method is based on the quartic Bézier approximation of circular arcs. We give the upper bound of Hausdorff distance between the conic section and the quartic Bézier curve, and also show that the approximation order is eight. And we prove that our approximation m... Show More
  • Oscillation of Second Order Nonlinear Differential Equations with a Damping Term

    Xue Mi, Ying Huang, Desheng Li

    Issue: Volume 5, Issue 2, April 2016
    Pages: 46-50
    Received: Mar. 23, 2016
    Accepted:
    Published: Mar. 25, 2016
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    Abstract: A class of second-order nonlinear differential equations with a damping term is investigated in this paper. By using the Riccati transformation technique and general weight functions, we obtain some new sufficient conditions for the oscillation of the equation. Our results improve and extend some known results. Two examples are given to illustrate ... Show More
  • The Stability of High Order Max-Type Difference Equation

    Han Cai-hong, Li Lue, Tan Xue

    Issue: Volume 5, Issue 2, April 2016
    Pages: 51-55
    Received: Apr. 06, 2016
    Accepted:
    Published: Apr. 07, 2016
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    Abstract: In this paper, we investigate the stability of following max-type difference equation , where , with , , and , the initial values are positive. By constructing a system of equations and binary function, we show the equation has a unique positive equilibrium solution, and the positive equilibrium solution is globally asymptotically stable. The conclusion of this paper extends and supplements the existing results.
  • Effect of Grid Step Sizes on Computational Time Using Finite-Difference Method for Seismic Wave Modeling

    Olowofela Joseph. A., Akinyemi Olukayode. D., Ajani Olumide. O.

    Issue: Volume 5, Issue 2, April 2016
    Pages: 56-63
    Received: Sep. 05, 2015
    Accepted: Sep. 21, 2015
    Published: Apr. 15, 2016
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    Abstract: Finite-difference method, a popular seismic forward modeling method is a technique which allows us to numerically solve partial differential equations like the wave equation solved in this paper. Beyond its use in standard data acquisition, it is a very instructive tool to understand how waves propagate in the earth's subsurface. Since the accuracy... Show More
  • Comparison Solutions Between Lie Group Method and Numerical Solution of (RK4) for Riccati Differential Equation

    Sami H. Altoum, Salih Y. Arbab

    Issue: Volume 5, Issue 2, April 2016
    Pages: 64-72
    Received: Feb. 17, 2016
    Accepted: Mar. 25, 2016
    Published: Apr. 15, 2016
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    Abstract: This paper introduced Lie group method as a analytical method and then compared to RK4 and Euler forward method as a numerical method. In this paper the general Riccati equation is solved by symmetry group. Numerical comparisons between exact solution, Lie symmetry group and RK4 on these equations are given. In particular, some examples will be con... Show More
  • Julia and Mandelbrot Sets of the Gamma Function Using Lanczos Approximation

    Richard Eneojo Amobeda, Terhemen Aboiyar, Solomon Ortwer Adee, Peter Vanenchii Ayoo

    Issue: Volume 5, Issue 2, April 2016
    Pages: 73-77
    Received: Mar. 20, 2016
    Accepted: Mar. 29, 2016
    Published: Apr. 15, 2016
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    Abstract: This work explores the Julia and Mandelbrot sets of the Gamma function by extending the function to the entire complex plane through analytic continuation and functional equations. Various Julia and Mandelbrot sets associated with the Gamma function are generated using the iterative function , with different parameter values. To produce an accurat... Show More
  • Tuncay Can’s Approximation Method to Obtain Initial Basic Feasible Solution to Transport Problem

    Tuncay Can, Habip Koçak

    Issue: Volume 5, Issue 2, April 2016
    Pages: 78-82
    Received: Apr. 14, 2016
    Accepted: Apr. 27, 2016
    Published: May 12, 2016
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    Abstract: Obtaining an initial basic feasible solution to a transport problem – or a corner point in the convex polytope region – is extremely important in terms of reaching the optimal solution to the problem in the shortest time. When a transport problem is basically accepted as a linear programming problem, a degenerated solution is caused by the structur... Show More
  • Application of Growth Functions to Describe the Dynamics of Avascular Tumor in Human Body

    Bayru Haftu Hindeya, Samba Narasimha Murthy

    Issue: Volume 5, Issue 2, April 2016
    Pages: 83-90
    Received: Apr. 20, 2016
    Accepted: Apr. 29, 2016
    Published: May 12, 2016
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    Abstract: This paper deals with the applications of mathematical growth functions such as monomolecular, time delay logistic and Gompertz functions to describe the dynamics of avascular tumor growth. In this case we analyze the steady state of the modified systems of the model using Jacobean matrix to show that it is stable on the nontrivial stationary point... Show More
  • Anti-periodic Boundary Value Problems of φ-Laplacian Impulsive Differential Equations

    Xiufeng Guo, Yuan Gu

    Issue: Volume 5, Issue 2, April 2016
    Pages: 91-96
    Received: May 03, 2016
    Accepted: May 13, 2016
    Published: May 30, 2016
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    Abstract: This paper concerned with the existence of solutions of anti-periodic boundary value problems for impulsive differential equations with φ-Laplacian operator. Firstly, the definition a pair of coupled lower and upper solutions of the problem is introduced. Then, under the approach of coupled upper and lower solutions together with Nagumo conditi... Show More