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The General Form of Linearized Exact Solution for the KdV Equation by the Simplest Equation Method
Sen-Yung Lee,
Chun-Ku Kuo
Issue:
Volume 4, Issue 5, October 2015
Pages:
335-341
Received:
29 June 2015
Accepted:
5 August 2015
Published:
19 August 2015
Abstract: The general form of linearized exact solution for the Korteweg and de Vries (KdV) equation, with an arbitrary nonlinear coefficient, is derived by the simplest equation method with the Bernoulli equation as the simplest equation. It is shown that the proposed exact solution overcomes the long existing problem of discontinuity and can be successfully reduced to linearity, while the nonlinear term coefficient approaches zero. Comparison of four different soliton solutions is presented. A new phenomenon, named soliton sliding, is observed.
Abstract: The general form of linearized exact solution for the Korteweg and de Vries (KdV) equation, with an arbitrary nonlinear coefficient, is derived by the simplest equation method with the Bernoulli equation as the simplest equation. It is shown that the proposed exact solution overcomes the long existing problem of discontinuity and can be successfull...
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On a Subclass of Close-to-Convex Functions Associated with Fixed Second Coefficient
Selvaraj Chellian,
Stelin Simpson,
Logu Sivalingam
Issue:
Volume 4, Issue 5, October 2015
Pages:
342-345
Received:
18 July 2015
Accepted:
3 August 2015
Published:
19 August 2015
Abstract: We consider a subclass of univalent functions f (z) for which there corresponds a convex function g(z) of order α such that Re(zf'(z) / g(z)) ≥ β. We investigate the influence of the second coefficient of g(z) on this class. We also prove distortion, covering, and radius of convexity theorems
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Numerical Study of Convective Heat Transfer on the Power Law Fluid over a Vertical Exponentially Stretching Cylinder
M. Naseer,
M. Y. Malik,
Abdul Rehman
Issue:
Volume 4, Issue 5, October 2015
Pages:
346-350
Received:
18 June 2015
Accepted:
27 June 2015
Published:
21 August 2015
Abstract: The present paper is the study of boundary layer flow and heat transfer of Power law fluid flowing over a vertical exponentially stretching cylinder along its axial direction. The governing partial differential equations and the associated boundary conditions are reduced to nonlinear ordinary differential equations after using the boundary layer approximation and similarity transformations. The obtained system of nonlinear ordinary differential equations subject to the boundary conditions is solved numerically with the help of Fehlberg method. The effects of Power law index , Reynolds number , Prandtl number , the natural convection parameter and local Reynolds number are presented through graphs. The skin friction coefficient and Nusselt number are presented through tables for different parameters.The present paper is the study of boundary layer flow and heat transfer of Power law fluid flowing over a vertical exponentially stretching cylinder along its axial direction. The governing partial differential equations and the associated boundary conditions are reduced to nonlinear ordinary differential equations after using the boundary layer approximation and similarity transformations. The obtained system of nonlinear ordinary differential equations subject to the boundary conditions is solved numerically with the help of Fehlberg method. The effects of Power law index , Reynolds number , Prandtl number , the natural convection parameter λ and local Reynolds number Rea are presented through graphs. The skin friction coefficient and Nusselt number are presented through tables for different parameters.
Abstract: The present paper is the study of boundary layer flow and heat transfer of Power law fluid flowing over a vertical exponentially stretching cylinder along its axial direction. The governing partial differential equations and the associated boundary conditions are reduced to nonlinear ordinary differential equations after using the boundary layer ap...
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Effect of Varying StepSizes in Numerical Approximation of Stochastic Differential Equations Using One Step Milstein Method
Sunday Jacob Kayode,
Akeem Adebayo Ganiyu
Issue:
Volume 4, Issue 5, October 2015
Pages:
351-362
Received:
13 August 2015
Accepted:
28 August 2015
Published:
9 September 2015
Abstract: This paper examines the effect of varying stepsizes in finding the approximate solution of stochastic differential equations (SDEs). One step Milstein method (MLSTM) for solution of general first order stochastic differential equations (SDEs) has been derived using Itô Lemma and Euler-Maruyama Method as supporting tools. Two problems in the form of first order SDEs have been considered. The method of solution used is one step Milstein method. The absolute errors were calculated using the exact solution and numerical solution. Comparison of varying the stepsizes was achieved using mean absolute error criterion. The results showed that the mean absolute error due to approximation decreases as the stepsizes decreases. The order of convergence is approximately 1, which indicates the accuracy of the method. Also, the effect of varying stepsizes can also be identified using graphical method constructed for various stepsizes.
Abstract: This paper examines the effect of varying stepsizes in finding the approximate solution of stochastic differential equations (SDEs). One step Milstein method (MLSTM) for solution of general first order stochastic differential equations (SDEs) has been derived using Itô Lemma and Euler-Maruyama Method as supporting tools. Two problems in the form of...
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Sensitivity Analysis of Parameters in a Competition Model
Frank Nathan Ngoteya,
Yaw Nkansah-Gyekye
Issue:
Volume 4, Issue 5, October 2015
Pages:
363-368
Received:
27 August 2015
Accepted:
8 September 2015
Published:
22 September 2015
Abstract: Competition models may be used by ecologists as basic guidelines in analyzing issues that contribute to the decline of species population. To be used for that purpose, a mathematical model must be prudently parameterized. Therefore, this paper examines the effects of interference competition by lions with human–related mortality to the population dynamics of African wild dogs. The model was carefully parameterized and validated with estimated data by employing the theory of basic reproduction number and by running the sensitivity analysis. Numerical simulation of the model was executed by using MATLAB to explore the outcome of certain key parameters when changes are applied on them.
Abstract: Competition models may be used by ecologists as basic guidelines in analyzing issues that contribute to the decline of species population. To be used for that purpose, a mathematical model must be prudently parameterized. Therefore, this paper examines the effects of interference competition by lions with human–related mortality to the population d...
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Application Chebyshev Polynomials for Determining the Eigenvalues of Sturm-Liouville Problem
Dong Yun Shen,
Yong Huang
Issue:
Volume 4, Issue 5, October 2015
Pages:
369-373
Received:
31 August 2015
Accepted:
11 September 2015
Published:
22 September 2015
Abstract: This paper discusses the eigenvalue problem of second-order Sturm-Liouville equation. We transform the governing differential equation to the Fredholm-Volterra integral equation with appropriate end supports. By expanding the unknown function into the shifted Chebyshev polynomials, we directly get the corresponding polynomial characteristic equations, where the lower and higher-order eigenvalues can be determined simultaneously from the multi-roots. Several examples of estimating eigenvalues are given. By comparison with the exact results in open literatures, the correctness and effectiveness of the present approach are verified.
Abstract: This paper discusses the eigenvalue problem of second-order Sturm-Liouville equation. We transform the governing differential equation to the Fredholm-Volterra integral equation with appropriate end supports. By expanding the unknown function into the shifted Chebyshev polynomials, we directly get the corresponding polynomial characteristic equatio...
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Modeling Oil Palm Nutrient Management Using Linear Goal Programming
Rida Agustina,
Habibis Saleh,
M. D. H. Gamal
Issue:
Volume 4, Issue 5, October 2015
Pages:
374-378
Received:
28 August 2015
Accepted:
11 September 2015
Published:
25 September 2015
Abstract: This paper describes a mathematical model for a good mixture of fertilizer levels using goal programming technique for oil palm plantations so that the oil palm plants produce high quality fruit. Goal programming used is preemptive goal programming. Computational results indicates that the determination of the optimal the mix of fertilizer using goal programming techniques is very effective because this technique is able to meet any goals expected in the oil palm plantations.
Abstract: This paper describes a mathematical model for a good mixture of fertilizer levels using goal programming technique for oil palm plantations so that the oil palm plants produce high quality fruit. Goal programming used is preemptive goal programming. Computational results indicates that the determination of the optimal the mix of fertilizer using go...
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The Impact of Increasing Input Costs to the Farmers in Cotton Production in Tanzania
Busheni Dome,
Dmitry Kuznetsov,
Yaw Nkansah-Gyekye
Issue:
Volume 4, Issue 5, October 2015
Pages:
379-386
Received:
28 August 2015
Accepted:
11 September 2015
Published:
25 September 2015
Abstract: The persistence of increasing input costs has effects to the farmers in the process of cotton production. These input costs can be in terms of pesticides, seeds, fertilizers, sprayers and the like, that have a real contribution towards cotton outputs per hectare. This paper intended to analyze effects of increasing input costs to the cotton farmers in Tanzania. The primary data were collected through questionnaires, which were distributed to 35 respondents, who are knowledgeable enough about cotton production in Shinyanga-Bariadi. Secondary data were collected from the Tanzania Cotton Board, Ukiliguru Agriculture Training Institute and Shinyanga Regional Commissioners. A log-linear model was estimated by using Panel data method consisting of 24 observations from Mwanza-Misungwi and Shinyanga-Bariadi from 2003 to 2014. The Hausman test was applied to evaluate the fixed effect and random effect by using STATA 11 and EXCEL. The elasticity for every variable was computed to evaluate how a change in input price might increase or decrease the costs to the cotton farmers in Tanzania.
Abstract: The persistence of increasing input costs has effects to the farmers in the process of cotton production. These input costs can be in terms of pesticides, seeds, fertilizers, sprayers and the like, that have a real contribution towards cotton outputs per hectare. This paper intended to analyze effects of increasing input costs to the cotton farmers...
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