Mathematical and Computational Applications

404 KiB

Open AccessArticle

The Darboux Trihedrons of Regular Curves on a Regular Time-Like Surface

by Emin Özyilmaz

Math. Comput. Appl. 2014, 19(2), 172-183; https://doi.org/10.3390/mca19020172 - 01 Aug 2014

Viewed by 1102

In this work, we study Differential Geometry in the Minkowski 3-space R₁³ of the curves on a time-like regular surface by using parameter curves which are not perpendicular to each other. The aim of this study is to investigate the formulae [...] Read more.

In this work, we study Differential Geometry in the Minkowski 3-space R₁³ of the curves on a time-like regular surface by using parameter curves which are not perpendicular to each other. The aim of this study is to investigate the formulae between the Darboux Vectors of the time-like curve (c) , the time-like parameter curve (c₁) and the space-like parameter curve (c₂) which are not intersecting perpendicularly. Full article

561 KiB

Open AccessArticle

Approximate Solutions for Coupled Systems of Nonlinear PDEs Using the Reduced Differential Transform Method

by Mahmoud Rawashdeh

Math. Comput. Appl. 2014, 19(2), 161-171; https://doi.org/10.3390/mca19020161 - 01 Aug 2014

Cited by 15 | Viewed by 1548

Abstract

In this paper, we are concerned with finding approximate solutions to systems of nonlinear PDEs using the Reduced Differential Transform Method (RDTM). We examine this method to obtain approximate numerical solutions for two different types of systems of nonlinear partial differential equations, such [...] Read more.

In this paper, we are concerned with finding approximate solutions to systems of nonlinear PDEs using the Reduced Differential Transform Method (RDTM). We examine this method to obtain approximate numerical solutions for two different types of systems of nonlinear partial differential equations, such as the two- component KdV evolutionary system of order two and the Broer-Kaup (BK) system of equations. The theoretical analysis of the RDTM is investigated for these systems of equations and is calculated in the form of power series with easily computable terms. Illustrative examples will be presented to support the proposed analysis. Full article

209 KiB

Open AccessArticle

On a New Solution of Fractional Differential Equation Using Complex Transform in the Unit Disk

by Rabha W. Ibrahim and Maslina Darus

Math. Comput. Appl. 2014, 19(2), 152-160; https://doi.org/10.3390/mca19020152 - 01 Aug 2014

Cited by 7 | Viewed by 1135

Abstract

The Möbius transform of fractional differential equation (Riccati type) is employed to construct new exact solutions for some nonlinear fractional differential equations. The fractional operators are taken in sense of the modified Srivastava-Owa fractal in the unit disk. Examples are illustrated for problems [...] Read more.

The Möbius transform of fractional differential equation (Riccati type) is employed to construct new exact solutions for some nonlinear fractional differential equations. The fractional operators are taken in sense of the modified Srivastava-Owa fractal in the unit disk. Examples are illustrated for problems in biology, economic and physics. Full article

663 KiB

Open AccessArticle

Estimation of Mucus Clearance in Pulmonary Airways by Means of a Regression Model

by Shahriar Shamil Uulu, Halil Rıdvan Öz, Ferhat Karaca and Cahit A. Evrensel

Math. Comput. Appl. 2014, 19(2), 144-151; https://doi.org/10.3390/mca19020144 - 01 Aug 2014

Cited by 1 | Viewed by 1168

Abstract

In this study, a multivariate regression analysis was performed on a dataset obtained from experimental tracheal model for mucus clearance in pulmonary airways. Several simulations have been done to verify the validity of the generated regression model. In general, the clearance of mucus [...] Read more.

In this study, a multivariate regression analysis was performed on a dataset obtained from experimental tracheal model for mucus clearance in pulmonary airways. Several simulations have been done to verify the validity of the generated regression model. In general, the clearance of mucus in the airways is achieved by the beating action of cilia inside the serous layer which is the primary means of removing inhaled particulates and airway debris from airways in healthy people. In this study, two types of mucus simulants are used in the experimental setup. Clearance distances of a teardrop shape simulant are measured for different velocities, slope angles and surfaces properties. On the obtained data by applying several genuine transformations we developed a multiple regression model that is able to predict clearance up to 86% accuracy. Simulations revealed several important data like direct relation between velocity and clearance and indirect relation between angle and clearance. Full article

276 KiB

Open AccessArticle

Simplified, Analytically Solvable Model Problem for Non-Analog Monte Carlo Methods

by Yiğit Çeçen and Mehmet Tombakoğlu

Math. Comput. Appl. 2014, 19(2), 134-143; https://doi.org/10.3390/mca19020134 - 01 Aug 2014

Viewed by 1094

Abstract

In Monte Carlo particle transport, it is important to change the variance of calculations of relatively rare events with a technique known as non-analog Monte Carlo. In order to reduce the variance and the computation time, biasing techniques are introduced to accelerate the [...] Read more.

In Monte Carlo particle transport, it is important to change the variance of calculations of relatively rare events with a technique known as non-analog Monte Carlo. In order to reduce the variance and the computation time, biasing techniques are introduced to accelerate the calculation convergence without changing the outcome. However these variance reduction techniques are often complex and can only be solved by computer codes. In this study, a simplified, analytically solvable model problem is introduced for non-analog Monte Carlo methods. A sample problem for neutrons passing through a thick shield is simulated. The drawback of this simulation is the expensive computation time and large variance for analog Monte Carlo methods. So, biasing techniques like implicit capture and splitting are introduced and the problem is solved analytically. Full article

665 KiB

Open AccessArticle

Analytical Solutions of Non-Linear Equations of Power-Law Fluids of Second Grade over an Infinite Porous Plate

by Saeid Abbasbandy, Muhammet Yürüsoy and Hüseyin Güllüce

Math. Comput. Appl. 2014, 19(2), 124-133; https://doi.org/10.3390/mca19020124 - 01 Aug 2014

Cited by 67 | Viewed by 2203

Abstract

The flow of an incompressible fluid of modified second grade past an infinite porous plate subject to either suction or blowing at the plate is studied. The model is a combination of power-law and second grade fluid in which the fluid may exhibit [...] Read more.

The flow of an incompressible fluid of modified second grade past an infinite porous plate subject to either suction or blowing at the plate is studied. The model is a combination of power-law and second grade fluid in which the fluid may exhibit normal stresses, shear thinning or shear thickening behaviors. Equations of motion in dimensionless form are derived. Analytical solutions of the outcoming non-linear differential equations are found by using the homotopy analysis method (HAM), which is a powerful semi-analytical method. Effects of power-law index and second grade coefficient on the boundary layers are shown and solutions are contrasted with the usual second grade fluid solutions. Full article

320 KiB

Open AccessArticle

A Note on Fractional Differential Subordination Based on the Srivastava-Owa Fractional Operator

by Rabha W. Ibrahim and Maslina Darus

Math. Comput. Appl. 2014, 19(2), 115-123; https://doi.org/10.3390/mca19020115 - 01 Aug 2014

Cited by 2 | Viewed by 1109

Abstract

In this work, we consider a definition for the concept of fractional differential subordination in sense of Srivastava-Owa fractional operators. By employing some types of admissible functions involving differential operator of fractional order, we illustrate applications. Full article

288 KiB

Open AccessArticle

Reliability Analysis of M/G/1 Repairable Queueing System with Multiple Adaptive Vacations and p-Entering Discipline

by Jiang Cheng and Yinghui Tang

Math. Comput. Appl. 2014, 19(2), 105-114; https://doi.org/10.3390/mca19020105 - 01 Aug 2014

Viewed by 1088

Abstract

This paper considers the reliability of an M/G/1 queue with multiple adaptive vacations in which the arriving customers enter the system with probability p (0＜p≤1) during vacations. Through appropriate assumptions, the model is studied by the total probability decomposition technique and the tool [...] Read more.

This paper considers the reliability of an M/G/1 queue with multiple adaptive vacations in which the arriving customers enter the system with probability p (0＜p≤1) during vacations. Through appropriate assumptions, the model is studied by the total probability decomposition technique and the tool of Laplace transform. Some reliability indices are studied. Moreover, we give some numerical examples to observe the effect of various parameters on the reliability indices. Full article

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Math. Comput. Appl., Volume 19, Issue 2 (August 2014) – 8 articles , Pages 105-183

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