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Asymptotic Method of Krylov-Bogoliubov-Mitropolskii for Fifth Order Critically Damped Nonlinear Systems
Md. Nazrul Islam,
Md. Mahafujur Rahaman,
M. Abul Kawser
Issue:
Volume 4, Issue 6, December 2015
Pages:
387-395
Received:
26 August 2015
Accepted:
19 September 2015
Published:
29 September 2015
Abstract: In oscillatory problems, the method of Krylov–Bogoliubov–Mitropolskii (KBM) is one of the most used techniques to obtain analytical approximate solution of nonlinear systems with a small non-linearity. This article modifies the KBM method to examine the solutions of fifth order critically damped nonlinear systems with four pairwise equal eigenvalues and one distinct eigenvalue, in which the latter eigenvalue is much larger than the former four pairwise eigenvalues. This paper suggests that the results obtained in this study correspond accurately to the numerical solutions obtained by the fourth order Runge-Kutta method. This paper, therefore, concludes that the modified KBM method provides highly accurate results, which can be applied for different kinds of nonlinear differential systems.
Abstract: In oscillatory problems, the method of Krylov–Bogoliubov–Mitropolskii (KBM) is one of the most used techniques to obtain analytical approximate solution of nonlinear systems with a small non-linearity. This article modifies the KBM method to examine the solutions of fifth order critically damped nonlinear systems with four pairwise equal eigenvalue...
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A Mathematical Model for Control and Elimination of the Transmission Dynamics of Measles
Stephen Edward,
Kitengeso Raymond E.,
Kiria Gabriel T.,
Felician Nestory,
Mwema Godfrey G.,
Mafarasa Arbogast P.
Issue:
Volume 4, Issue 6, December 2015
Pages:
396-408
Received:
10 August 2015
Accepted:
7 September 2015
Published:
29 September 2015
Abstract: Despite the availability of measles vaccine since 1963, the infectious disease is still endemic in many parts of the world including developed nations. Elimination of measles requires maintaining the effective reproduction number less than unity, Re <1 as well as achieving low levels of susceptibility. Infectious diseases are great field for mathematical modeling, and for connecting mathematical models to primary or secondary data. In this project, we concentrated on the mathematical model for control and elimination of transmission dynamics of measles. We have obtained disease free equilibrium (DFE) point, effective reproduction number and basic reproduction number for the model. Simulations of different variables of the model have been performed and sensitivity analysis of different embedded parameters has been done. MATLAB has been used in simulations of the ordinary differential equations (ODEs) as well as the reproduction numbers.
Abstract: Despite the availability of measles vaccine since 1963, the infectious disease is still endemic in many parts of the world including developed nations. Elimination of measles requires maintaining the effective reproduction number less than unity, Re <1 as well as achieving low levels of susceptibility. Infectious diseases are great field for mat...
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Modeling the Dynamics of Rabies Transmission with Vaccination and Stability Analysis
Tesfaye Tadesse Ega,
Livingstone S. Luboobi,
Dmitry Kuznetsov
Issue:
Volume 4, Issue 6, December 2015
Pages:
409-419
Received:
7 September 2015
Accepted:
21 September 2015
Published:
10 October 2015
Abstract: In this paper we formulate a deterministic mathematical model for the transmission dynamics of rabies in human and animal within and around Addis Ababa, Ethiopia. Our model involves vaccination program for dog population. The basic reproduction number and effective reproduction numbers are computed and the results are entirely depending on the parameters of dog population, which shows the responsibility of dog population for human and livestock infection. For a specified set of values of parameters as deduced from the data provided by Ethiopian Public Health Institute of Addis Ababa, the basic reproduction number R0 and the effective reproduction number Re works out to be 2 and 1.6 respectively, which indicates the disease will be endemic. The numerical simulation of reproduction ratio shows that the combination of vaccination, culling of stray dogs and controlling annual crop of new born puppies are the best method to control rabies transmission within and around Adds Ababa. The disease - free equilibrium ε0 is computed. When the effective reproduction number Re<1 it is proved to be globally asymptotically stable in the feasible region Φ. When Re>1 there exists one endemic equilibrium point which is locally asymptotically stable.
Abstract: In this paper we formulate a deterministic mathematical model for the transmission dynamics of rabies in human and animal within and around Addis Ababa, Ethiopia. Our model involves vaccination program for dog population. The basic reproduction number and effective reproduction numbers are computed and the results are entirely depending on the pa...
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A New Straightforward Method for Evaluating Singular Integrals
Md. Habibur Rahaman,
Md. Ashraful Huq,
M. Kamrul Hasan
Issue:
Volume 4, Issue 6, December 2015
Pages:
420-423
Received:
27 May 2015
Accepted:
3 June 2015
Published:
13 October 2015
Abstract: A new more accurate straightforward method is presented for evaluating the singular integrals. A few methods in numerical analysis is useful for evaluating the integral where singularities arises, most of them uses extrapolation technique at singular point. This new method uses directly and gives better results and the Romberg integration of this formula converses faster than others previous methods.
Abstract: A new more accurate straightforward method is presented for evaluating the singular integrals. A few methods in numerical analysis is useful for evaluating the integral where singularities arises, most of them uses extrapolation technique at singular point. This new method uses directly and gives better results and the Romberg integration of this f...
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Boundary Layer Flow and Heat Transfer of Micropolar Fluid over a Vertical Exponentially Stretched Cylinder
Abdul Rehman,
Razmak Bazai,
Sallahuddin Achakzai,
Saleem Iqbal,
Muhammad Naseer
Issue:
Volume 4, Issue 6, December 2015
Pages:
424-430
Received:
14 September 2015
Accepted:
26 September 2015
Published:
15 October 2015
Abstract: The current paper offers an analysis of the steady boundary layer flow and heat transfer of a non-Newtonian micropolar fluid flowing through a vertical exponentially stretching cylinder along its axial axis. The obtained system of nonlinear partial differential equations along with the appropriate boundary conditions is abridged to dimensionless form by means of the boundary layer estimates and a suitable similarity transformation. The subsequent nonlinear coupled system of ordinary differential equations subject to the appropriate boundary conditions is solved numerically with the help of Keller-box method. The effects of the involved parameters are presented through graphs. The allied physical features for the flow and heat transfer characteristics that is the skinfriction coefficient and Nusselt numbers are presented for different parameters.
Abstract: The current paper offers an analysis of the steady boundary layer flow and heat transfer of a non-Newtonian micropolar fluid flowing through a vertical exponentially stretching cylinder along its axial axis. The obtained system of nonlinear partial differential equations along with the appropriate boundary conditions is abridged to dimensionless fo...
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Modeling and Stability Analysis for Measles Metapopulation Model with Vaccination
Leopard C. Mpande,
Damian Kajunguri,
Emmanuel A. Mpolya
Issue:
Volume 4, Issue 6, December 2015
Pages:
431-444
Received:
11 September 2015
Accepted:
26 September 2015
Published:
23 October 2015
Abstract: In this paper, a metapopulation model is formulated as a system of ordinary differential equations to study the impact of vaccination on the spread of measles. The disease-free equilibrium is computed and proved to be locally and globally asymptotically stable if RC <1 and unstable if RC >1. We show that when there are no movements between the two patches, there exists at least one endemic equilibrium for all RCi >1 and bifurcation analysis of endemic equilibrium point proves that forward (supercritical) bifurcation occurs in each patch. Numerical simulation results are also presented to validate analytical results and to show the impact of vaccination on the incidence and prevalence of measles in a metapopulation.
Abstract: In this paper, a metapopulation model is formulated as a system of ordinary differential equations to study the impact of vaccination on the spread of measles. The disease-free equilibrium is computed and proved to be locally and globally asymptotically stable if RC <1 and unstable if RC >1. We show that when there are no movements between th...
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FD-RBF for Partial Integro-Differential Equations with a Weakly Singular Kernel
Jafar Biazar,
Mohammad Ali Asadi
Issue:
Volume 4, Issue 6, December 2015
Pages:
445-451
Received:
25 September 2015
Accepted:
7 October 2015
Published:
23 October 2015
Abstract: Finite Difference Method and Radial Basis Functions are applied to solve partial integro-differential equations with a weakly singular kernel. The product trapezoidal method is used to compute singular integrals that appear in the discretization process. Different RBFs are implemented and satisfactory results are shown the ability and the usefulness of the proposed method.
Abstract: Finite Difference Method and Radial Basis Functions are applied to solve partial integro-differential equations with a weakly singular kernel. The product trapezoidal method is used to compute singular integrals that appear in the discretization process. Different RBFs are implemented and satisfactory results are shown the ability and the usefulnes...
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DIAGRID Generation Applied to X-shape Steel Tube of HSA800 with High Tensile Strength and Ductility
Issue:
Volume 4, Issue 6, December 2015
Pages:
452-455
Received:
16 October 2014
Accepted:
30 October 2014
Published:
17 November 2015
Abstract: This article proposes DIAGRID structural details locked in X-formed steel tube using HSA 800 steel with high tensile strength and superior ductility as a modification of an original DIAGRID version. The structural effectiveness of the new structural DIAGRID detail information is presented in this study using actual nonlinear static pushover analysis.
Abstract: This article proposes DIAGRID structural details locked in X-formed steel tube using HSA 800 steel with high tensile strength and superior ductility as a modification of an original DIAGRID version. The structural effectiveness of the new structural DIAGRID detail information is presented in this study using actual nonlinear static pushover analysi...
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Comparison of ARIMA Model and Exponential Smoothing Model on 2014 Air Quality Index in Yanqing County, Beijing, China
Jie Zhu,
Ruoling Zhang,
Binbin Fu,
Renhao Jin
Issue:
Volume 4, Issue 6, December 2015
Pages:
456-461
Received:
1 November 2015
Accepted:
9 November 2015
Published:
19 November 2015
Abstract: In order to study the changes of air quality index (AQI) in Yanqing County, Beijing, China and predict the trend of AQI value, this paper constructed a time-series analysis．A non-stationary trend is found, and the ARIMA (1, 1, 2) model and Holt exponential smoothing model are found to sufficiently model the data. In comparison of these two model fittings, the ARIMA modelling result are better than Holt modelling’s in terms of trend capturing and result MSE, and in this data it is better to apply the ARIMA model to predict the future AQI values.
Abstract: In order to study the changes of air quality index (AQI) in Yanqing County, Beijing, China and predict the trend of AQI value, this paper constructed a time-series analysis．A non-stationary trend is found, and the ARIMA (1, 1, 2) model and Holt exponential smoothing model are found to sufficiently model the data. In comparison of these two model fi...
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Reliability Based Optimization with Metaheuristic Algorithms and Latin Hypercube Sampling Based Surrogate Models
Liu Chu,
Eduardo Souza De Cursi,
Abdelkhalak El Hami,
Mohamed Eid
Issue:
Volume 4, Issue 6, December 2015
Pages:
462-468
Received:
20 November 2015
Accepted:
29 November 2015
Published:
18 December 2015
Abstract: Reliability based optimization (RBO) is one of the most appropriate methods for structural design under uncertainties. It searches for the best compromise between cost and safety while considering system uncertainties by incorporating reliability measures within the optimization. Despite the advantages of RBO, its application to practical engineering problem is still quite challenging. In this paper, we propose an effective method to decouple the loops of reliability assessment analysis and optimization by creating surrogate models. The Latin Hypercube sampling approach is applied to a structural finite element model to obtain an effective database for building surrogate models. In order to avoid premature convergence of the optimization process, the RBO problem is solved with metaheuristic methods such as genetic algorithm and simulated annealing. The relative efficiency of surrogate models and their relationship with metaheuristic search engine are discussed in the article.
Abstract: Reliability based optimization (RBO) is one of the most appropriate methods for structural design under uncertainties. It searches for the best compromise between cost and safety while considering system uncertainties by incorporating reliability measures within the optimization. Despite the advantages of RBO, its application to practical engineeri...
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