Mathematical and Computational Applications

277 KiB

Open AccessArticle

Asymptotic Solutions and Comparisons of a Generalized Van Del Pol Oscillator with Slowly Varying Parameter

by Ping Cai and Jianping Cai

Math. Comput. Appl. 2009, 14(2), 159-168; https://doi.org/10.3390/mca14020159 - 01 Aug 2009

Cited by 1 | Viewed by 1115

A generalized Van del Pol oscillator with slowly varying parameter is studied. The leading order approximate solutions are obtained respectively by three methods and comparisons are made with numerical results. Different amplitudes are also made to compare the accuracy of the three methods. [...] Read more.

A generalized Van del Pol oscillator with slowly varying parameter is studied. The leading order approximate solutions are obtained respectively by three methods and comparisons are made with numerical results. Different amplitudes are also made to compare the accuracy of the three methods. Full article

190 KiB

Open AccessArticle

Application of the Variational Iteration Method for System of Nonlinear Volterra’s Integro-Differential Equations

by Saeid Abbasbandy and Elyas Shivanian

Math. Comput. Appl. 2009, 14(2), 147-158; https://doi.org/10.3390/mca14020147 - 01 Aug 2009

Cited by 26 | Viewed by 1553

Abstract

In this paper, the variational iteration method is proposed to solve system of nonlinear Volterra's integro-differential equations. Four numerical examples are illustrated by this method. The results reveal that this method is very effective and highly promising in comparison with other numerical methods. [...] Read more.

In this paper, the variational iteration method is proposed to solve system of nonlinear Volterra's integro-differential equations. Four numerical examples are illustrated by this method. The results reveal that this method is very effective and highly promising in comparison with other numerical methods. Full article

329 KiB

Open AccessArticle

A Graphical User Interface for Programming Stepper Motors Used at Different Kinds of Applications

by Ahmet Altintas

Math. Comput. Appl. 2009, 14(2), 139-146; https://doi.org/10.3390/mca14020139 - 01 Aug 2009

Cited by 4 | Viewed by 1511

Abstract

Stepper motors are a digital actuator whose input is in the form of programmed energization of the stator windings and whose output is in the form of discrete angular rotation. It is, therefore, ideally suited for use as an actuator in computer control [...] Read more.

Stepper motors are a digital actuator whose input is in the form of programmed energization of the stator windings and whose output is in the form of discrete angular rotation. It is, therefore, ideally suited for use as an actuator in computer control systems, digital control systems and etc. Control systems employing stepper motors as actuators are known as incremental motion control systems. In this study both a GUI and a programming page driven from Matlab program are developed for programming and controlling different types of stepper motors at different drive modes. The parallel port of a PC is used to drive stepper motors. By means of this software, stepper motors having up to 8-separate-excitating signal can be programmable and controllable easily. In the software many different rotational motions are defined as built–in functions. In addition, it provides that the user can define new built-in functions, too. It can be, also, considered as a learning aid system for students to get a comprehensive understanding of stepper motors. Full article

153 KiB

Open AccessArticle

Discrete Singular Convolution for Free Vibration Analysis Annular Membranes

by Ömer Civalek and Murat Gürses

Math. Comput. Appl. 2009, 14(2), 131-138; https://doi.org/10.3390/mca14020131 - 01 Aug 2009

Cited by 9 | Viewed by 1180

Abstract

In this paper, we investigate the effects of some geometric parameters and density variation on frequency characteristics of the annular membranes with varying density. The discrete singular convolution method based on regularized Shannon’s delta kernel is applied to obtain the frequency parameter. The [...] Read more.

In this paper, we investigate the effects of some geometric parameters and density variation on frequency characteristics of the annular membranes with varying density. The discrete singular convolution method based on regularized Shannon’s delta kernel is applied to obtain the frequency parameter. The obtained results have been compared with the analytical and numerical results of other researchers, which showed well agreement. Full article

210 KiB

Open AccessArticle

Operating System Selection Using Fuzzy AHP and TOPSIS Methods

by Serkan Ballı and Serdar Korukoğlu

Math. Comput. Appl. 2009, 14(2), 119-130; https://doi.org/10.3390/mca14020119 - 01 Aug 2009

Cited by 116 | Viewed by 4174

Abstract

The aim of study is developing a fuzzy decision model to select appropriate operating system for computer systems of the firms by taking subjective judgments of decision makers into consideration. Proposed approach is based on Fuzzy Analytic Hierarchy Process (FAHP) and TOPSIS (Technique [...] Read more.

The aim of study is developing a fuzzy decision model to select appropriate operating system for computer systems of the firms by taking subjective judgments of decision makers into consideration. Proposed approach is based on Fuzzy Analytic Hierarchy Process (FAHP) and TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) methods. FAHP method is used in determining the weights of the criteria by decision makers and then rankings of the operating systems are determined by TOPSIS method. Empirical study has also been demonstrated. Full article

445 KiB

Open AccessArticle

Designing Optimum Oil Thickness in Artificial Human Knee Joint by Simulated Annealing

by Hamit Saruhan

Math. Comput. Appl. 2009, 14(2), 109-117; https://doi.org/10.3390/mca14020109 - 01 Aug 2009

Cited by 8 | Viewed by 1237

Abstract

In human knee joints, synovial fluid film covers the surface of synovium and cartilage within the joint space. Synovial joints acts as bearing in mechanical system. Although the artificial human joints differ from most mechanical bearings in their nature, they have been modeled [...] Read more.

In human knee joints, synovial fluid film covers the surface of synovium and cartilage within the joint space. Synovial joints acts as bearing in mechanical system. Although the artificial human joints differ from most mechanical bearings in their nature, they have been modeled and analyzed in terms of hydrodynamic bearing of engineering. In this study, nature inspired an algorithm, the simulated annealing (SA), is used to find minimum fluid film thickness in artificial human knee joints. It is important to optimize the film thickness of the bearing in terms of successful operation and lifetime of the implant in terms of friction and wear. The problem is complex and a time consuming process due to design variables and constraints imposed on the objective function. It is demonstrated that the SA performed and obtained convergence reliability on the optimum point. Full article

736 KiB

Open AccessArticle

Numerical Modeling of Venturi Flows for Determining Air Injection Rates Using Fluent V6.2

by Ahmet Baylar, M. Cihan Aydin, Mehmet Unsal and Fahri Ozkan

Math. Comput. Appl. 2009, 14(2), 97-108; https://doi.org/10.3390/mca14020097 - 01 Aug 2009

Cited by 33 | Viewed by 3292

Abstract

As the water passes through a restriction in a pipe, it forms a vacuum at the end of the restriction. A hole bored into the pipe at a point where this vacuum occurs will cause air to be drawn into the main flow. [...] Read more.

As the water passes through a restriction in a pipe, it forms a vacuum at the end of the restriction. A hole bored into the pipe at a point where this vacuum occurs will cause air to be drawn into the main flow. One example of this mechanism is seen in the venturi tube. When a minimal amount of differential pressure exists between the inlet and outlet sides of the venturi tube, a vacuum occurs at suction holes of the venturi tube. Venturi aeration is a method of aeration that has become popular in recent years. In present paper, air injection rates of venturi tubes are analyzed using Computational Fluid Dynamics modeling. These analyses are carried out by means of the program FLUENT V6.2 that uses finite volume theory. There is a good agreement between the measured air injection rates and the values computed from FLUENT CFD program. Full article

371 KiB

Open AccessArticle

Homotopy Perturbation Method for Solving Human T-Cell Lymphotropic Virus I(HTLV-I) Infection of Cd4+ T-Cells Model

by Mehmet Merdan

Math. Comput. Appl. 2009, 14(2), 85-96; https://doi.org/10.3390/mca14020085 - 01 Aug 2009

Cited by 1 | Viewed by 1349

Abstract

In this article, homotopy perturbation method is implemented to give approximate and analytical solutions of nonlinear ordinary differential equation systems such as human Tcell lymphotropic virus I (HTLV-I) infection of CD4+ T-cells model. The proposed scheme is based on homotopy perturbation method (HPM), [...] Read more.

In this article, homotopy perturbation method is implemented to give approximate and analytical solutions of nonlinear ordinary differential equation systems such as human Tcell lymphotropic virus I (HTLV-I) infection of CD4+ T-cells model. The proposed scheme is based on homotopy perturbation method (HPM), Laplace transform and Padé approximants. The results to get the homotopy perturbation method (HPM) is applied Padé approximants. Our proposed approach showed results to analytical solutions of nonlinear ordinary differential equation systems. Some plots are presented to show the reliability and simplicity of the methods. Full article

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Math. Comput. Appl., Volume 14, Issue 2 (August 2009) – 8 articles , Pages 85-168

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