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Volume 16
Issue 4
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Mathematical and Computational Applications is published by MDPI from Volume 21 Issue 1 (2016). Previous articles were published by another publisher in Open Access under a CC-BY (or CC-BY-NC-ND) licence, and they are hosted by MDPI on mdpi.com as a courtesy and upon agreement with the previous journal publisher.

Math. Comput. Appl., Volume 16, Issue 4 (December 2011) – 19 articles , Pages 784-979

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92 KiB  
Erratum
Erratum To: "High-Order Finite Difference Schemes for Solving the Advection-Diffusion Equation, Mathematical and Computational Applications, Vol. 15, No. 3, 449-460, 2010."
by Murat Sari, Gürhan Gürarslan and Asuman Zeytinoğlu
Math. Comput. Appl. 2011, 16(4), 979; https://doi.org/10.3390/mca16040979 - 01 Dec 2011
Viewed by 1000
Abstract
There are two points mistyped in the paper need to be changed as follows: [...]
Full article
143 KiB  
Article
Application of Chebyshev Approximation in the Process of Variational Iteration Method for Solving Differentialalgebraic Equations
by M. Ghovatmand, M.M. Hosseini and M. Nilli
Math. Comput. Appl. 2011, 16(4), 969-978; https://doi.org/10.3390/mca16040969 - 01 Dec 2011
Viewed by 1066
Abstract
In this paper, we use Chebyshev approximations in the process of He’s variational iteration method for finding the solution of differential-algebraic equations. This allows us to make integration at each of the iterations possible and at the same time, obtain a good accuracy [...] Read more.
In this paper, we use Chebyshev approximations in the process of He’s variational iteration method for finding the solution of differential-algebraic equations. This allows us to make integration at each of the iterations possible and at the same time, obtain a good accuracy in a reasonable number of iterations. Numerical results show that using Chebyshev approximation is much more efficient than using Taylor approximation which is more popular. First, an index reduction technique is implemented for semi-explicit differentialalgebraic equations, then the obtained problem is solved by He’s variational iteration method. The scheme is tested for some high index differential-algebraic equations and the results demonstrate reliability and efficiency of the proposed method. Full article
351 KiB  
Article
On the Coupling of Auxiliary Parameter, Adomian's Polynomials and Correction Functional
by M. M. Hosseini, Syed Tauseef Mohyud-Din and H. Ghaneai
Math. Comput. Appl. 2011, 16(4), 959-968; https://doi.org/10.3390/mca16040959 - 01 Dec 2011
Cited by 4 | Viewed by 1116
Abstract
In this paper, we apply He’s variational iteration method (VIM) coupled with an auxiliary parameter and Adomian’s polynomials which proves very effective to control the convergence region of approximate solution. The proposed algorithm is tested on generalized Hirota–Satsuma coupled KdV equation and numerical [...] Read more.
In this paper, we apply He’s variational iteration method (VIM) coupled with an auxiliary parameter and Adomian’s polynomials which proves very effective to control the convergence region of approximate solution. The proposed algorithm is tested on generalized Hirota–Satsuma coupled KdV equation and numerical results explicitly reveal the complete reliability, efficiency and accuracy of the suggested technique. It is observed that the approach may be implemented on other nonlinear models of physical nature. Full article
1114 KiB  
Article
Nonlinear Finite Element Analysis of an R/C Frame Under Lateral Loading
by Yunus Dere and Fatma Tuba Dede
Math. Comput. Appl. 2011, 16(4), 947-958; https://doi.org/10.3390/mca16040947 - 01 Dec 2011
Cited by 8 | Viewed by 1540
Abstract
Recent developments in computer technology have made possible the use of finite element methods for 3D modeling and analysis of reinforced concrete structures. In this study, the failure behavior and crack formation of an R/C frame under monotonic and reversed-cyclic lateral loading are [...] Read more.
Recent developments in computer technology have made possible the use of finite element methods for 3D modeling and analysis of reinforced concrete structures. In this study, the failure behavior and crack formation of an R/C frame under monotonic and reversed-cyclic lateral loading are studied by 3D nonlinear finite element analysis using ANSYS software. Modeling the nonlinear behavior of concrete material as well as the reinforcing steel embedded within concrete is a difficult task. Different methodologies and modeling options are considered in the computer model. The application of reversed cyclic displacement loading and the execution of nonlinear analyses are explained in detail. Load-displacement relationships and concrete crack profiles are obtained in order to compare with the experimental data and observed crack profile. The analysis results compared well with the experimental data based on the comparison of load-displacement graphs. The failure mode of the frame is identified by the crack profiles displayed on the structure. Full article
154 KiB  
Article
Numerical Solution of N-Order Fuzzy Differential Equations by Runge-Kutta Method
by S. Abbasbandy, T. Allahviranloo and P. Darabi
Math. Comput. Appl. 2011, 16(4), 935-946; https://doi.org/10.3390/mca16040935 - 01 Dec 2011
Cited by 15 | Viewed by 1241
Abstract
In this paper we study a numerical method for n-th order fuzzy differential equations based on Seikkala derivative with initial value conditions. The Runge-Kutta method is used for the numerical solution of this problem and the convergence and stability of the method [...] Read more.
In this paper we study a numerical method for n-th order fuzzy differential equations based on Seikkala derivative with initial value conditions. The Runge-Kutta method is used for the numerical solution of this problem and the convergence and stability of the method is proved. By this method, we can obtain strong fuzzy solution. This method is illustrated by solving some examples. Full article
580 KiB  
Article
Inequivalence of Classes of Linearizable Systems of Second Order Ordinary Differential Equations Obtained by Real and Complex Symmetry Analysis
by M. Safdar, Asghar Qadir and S. Ali
Math. Comput. Appl. 2011, 16(4), 923-934; https://doi.org/10.3390/mca16040923 - 01 Dec 2011
Cited by 13 | Viewed by 1062
Abstract
Linearizability criteria for systems of two cubically semi-linear second order ordinary differential equations (ODEs) were obtained by geometric means using real symmetry analysis (RSA). Separately, complex symmetry analysis (CSA) was developed to provide means to discuss systems of two ODEs. It was shown [...] Read more.
Linearizability criteria for systems of two cubically semi-linear second order ordinary differential equations (ODEs) were obtained by geometric means using real symmetry analysis (RSA). Separately, complex symmetry analysis (CSA) was developed to provide means to discuss systems of two ODEs. It was shown that CSA provides a class of linearizable systems of two cubically semi-linear ODEs. Linearizability criteria for this class were also developed. It is proved that the two classes of linearizable systems of two ODEs, provided by CSA and RSA, are inequivalent under point transformations. Full article
208 KiB  
Article
On the Application of New Convergence Criteria for Kantorovich Method to Nonlinear Singular Integral Equation with Shift
by Mohamed M. Allan and Smah M. Dardery
Math. Comput. Appl. 2011, 16(4), 913-922; https://doi.org/10.3390/mca16040913 - 01 Dec 2011
Viewed by 952
Abstract
The paper is concerned with the applicability of some new conditions for the convergence of Newton–kantorovich approximations to solution of nonlinear singular integral equation with shift of Uryson type. The results are illustrated in generalized Holder space. Full article
219 KiB  
Article
Properties of Symmetric Uclear Matter with Skyrme Iteractios
by Ahmet Biçer and Kaan Manisa
Math. Comput. Appl. 2011, 16(4), 900-912; https://doi.org/10.3390/mca16040900 - 01 Dec 2011
Cited by 1 | Viewed by 1141
Abstract
Symmetric nuclear matter properties such as binding energy, pressure, saturation density and incompressibility are investigated in the Skyrme Hartree-Fock model. A new set of Skyrme parameters for symmetric nuclear matter is obtained by the fitting of Variational Monte Carlo method results to density-dependent [...] Read more.
Symmetric nuclear matter properties such as binding energy, pressure, saturation density and incompressibility are investigated in the Skyrme Hartree-Fock model. A new set of Skyrme parameters for symmetric nuclear matter is obtained by the fitting of Variational Monte Carlo method results to density-dependent Skyrme type energy. The results obtained are in good agreement with those obtained with selected Skyrme parameter sets in the literature. Full article
538 KiB  
Article
A New Perturbation-Iteration Approach for First Order Differential Equations
by Mehmet Pakdemirli, Yiğit Aksoy and Hakan Boyacı
Math. Comput. Appl. 2011, 16(4), 890-899; https://doi.org/10.3390/mca16040890 - 01 Dec 2011
Cited by 19 | Viewed by 1449
Abstract
Two new perturbation-iteration algorithms for solving differential equations of first order are proposed. Variants of the algorithm are developed depending on the differential order of Taylor series expansions. The iteration algorithms are tested on a number of first order equations. Much better solutions [...] Read more.
Two new perturbation-iteration algorithms for solving differential equations of first order are proposed. Variants of the algorithm are developed depending on the differential order of Taylor series expansions. The iteration algorithms are tested on a number of first order equations. Much better solutions than the regular perturbation solutions are achieved. Full article
300 KiB  
Article
Forced Vibrations of Strongly Nonlinear Systems with Multiple Scales Lindstedt Poincaré Method
by M. Pakdemirli, M. M. F. Karahan and H. Boyacı
Math. Comput. Appl. 2011, 16(4), 879-889; https://doi.org/10.3390/mca16040879 - 01 Dec 2011
Cited by 27 | Viewed by 1476
Abstract
Forced vibrations of duffing equation with damping is considered. Recently developed Multiple Scales Lindstedt-Poincare (MSLP) technique for free vibrations is applied for the first time to the forced vibration problem in search of approximate solutions. For the case of weak and strong nonlinearities, [...] Read more.
Forced vibrations of duffing equation with damping is considered. Recently developed Multiple Scales Lindstedt-Poincare (MSLP) technique for free vibrations is applied for the first time to the forced vibration problem in search of approximate solutions. For the case of weak and strong nonlinearities, approximate solutions of the new method are contrasted with the usual Multiple Scales (MS) method and numerical simulations. For weakly nonlinear systems, frequency response curves of both perturbation methods and numerical solutions are in good agreement. For strongly nonlinear systems however, results of MS deviate much from the MSLP method and numerical simulations, the latter two being in good agreement. Full article
2261 KiB  
Article
Strengthening of RC Beams with Prefabricated RC Rectangular Cross-Sectional Plates
by M. Tekin, A. Demir, T. Turalı, H. Nohutçu and M. Bağcı
Math. Comput. Appl. 2011, 16(4), 868-878; https://doi.org/10.3390/mca16040868 - 01 Dec 2011
Viewed by 1145
Abstract
The topic of this study is to strengthen cracked beams with prefabricated RC rectangular cross-sectional plates. The damaged beams were repaired by epoxy based glue. The repaired beams were strengthened using prefabricated RC rectangular crosssectional plates. The strengthening plates were bonded to the [...] Read more.
The topic of this study is to strengthen cracked beams with prefabricated RC rectangular cross-sectional plates. The damaged beams were repaired by epoxy based glue. The repaired beams were strengthened using prefabricated RC rectangular crosssectional plates. The strengthening plates were bonded to the bottom face of the beams by anchorage rods and epoxy. The strengthened beams were incrementally loaded up to maximum load capacities. The experimental results were satisfactory since the load carrying capacities of damaged beams were increased approximately 47% due to strengthening. The post-elastic strength enhancement and the displacement ductility of all the beams are researched during the experiments. The experimental program was supported by a three-dimensional nonlinear finite element analysis. The experimental results were compared with the results obtained from the beam modeled with ANSYS finite element program. Full article
193 KiB  
Article
Classical Differential Geometry of Curves According to Type-2 Bishop Trihedra
by Emin Özyılmaz
Math. Comput. Appl. 2011, 16(4), 858-867; https://doi.org/10.3390/mca16040858 - 01 Dec 2011
Cited by 9 | Viewed by 1406
Abstract
In this work, we study classical differential geometry of the curves according to type-2 Bishop trihedra. First, we present some characterizations of a general helix, a helix, special cases and spherical curves. Thereafter, we investigate position vector of a regular curve by a [...] Read more.
In this work, we study classical differential geometry of the curves according to type-2 Bishop trihedra. First, we present some characterizations of a general helix, a helix, special cases and spherical curves. Thereafter, we investigate position vector of a regular curve by a system of ordinary differential equations whose solution gives the components of the position vector with respect to type-2 Bishop frame. Next we prove that the first vector field of the type-2 Bishop frame of a regular curve satisfies a vector differential equation of third order. Solutions of the mentioned system and vector differential equation have not been found. Therefore we present some special characterizations introducing special planes of three dimensional Euclidean space. Full article
798 KiB  
Article
Elastic-Plastic and Residual Stresses in Clamped Thermoplastic Composite Laminates Loaded Transversely
by Semih Benli, Mustafa Karamolla, Fuat Okumus and Onur Sayman
Math. Comput. Appl. 2011, 16(4), 849-857; https://doi.org/10.3390/mca16040849 - 01 Dec 2011
Viewed by 1052
Abstract
In this study, an elastic-plastic stress analysis was carried out in woven steel fibers- thermoplastic clamped composite laminates. The stacking sequences were chosen as [0/0]2, [15/-15]2, [30/-30]2 and [45/-45]2 for woven steel fibers – thermoplastic composites plates. [...] Read more.
In this study, an elastic-plastic stress analysis was carried out in woven steel fibers- thermoplastic clamped composite laminates. The stacking sequences were chosen as [0/0]2, [15/-15]2, [30/-30]2 and [45/-45]2 for woven steel fibers – thermoplastic composites plates. The layers were chosen for symmetric and antisymmetric cases. The finite element solution was performed by using the ANSYS software. Solid 186 element was utilized in the solution. Normal stress components at the clamped edges were found to be higher than that at the mid point of the laminated plates. Normal stresses are tensile at the mid point of the clamped edges and compressive at the mid point of the laminated plates. Then, the residual stress components were calculated in the critical points of the composite laminates. Full article
200 KiB  
Article
On Constitutive Equations for Anisotropic Nonlinearly Piezoelectric Materials
by Melek Usal and Lokman Yünlü
Math. Comput. Appl. 2011, 16(4), 839-848; https://doi.org/10.3390/mca16040839 - 01 Dec 2011
Cited by 2 | Viewed by 1259
Abstract
In this paper, the elastic-piezoelectric continuum has been investigated theoretically and its non-linear constitutive equations have been defined. The theory is formulated in the context of continuum electrodynamics. The solid medium is assumed to be non-linear, homogeneous, compressible and isothermal, has elastic and [...] Read more.
In this paper, the elastic-piezoelectric continuum has been investigated theoretically and its non-linear constitutive equations have been defined. The theory is formulated in the context of continuum electrodynamics. The solid medium is assumed to be non-linear, homogeneous, compressible and isothermal, has elastic and piezoelectric anisotropy. Basic principles of modern continuum mechanics and balance equations of electrostatic have provided guidance and have been determining in the process of this study. From the formulation belonging to the constitutive equations, it has been observed that the symmetric stress and polarization have been derived from a scalar-valued thermodynamic potential defined in calculations. As a result of thermodynamic constraints, it has been determined that the free energy function is dependent on a symmetric tensor and a vector. The free energy function has been represented by a power series expansion and the type and number of terms taken into consideration in this series expansion has determined the non-linearity of the medium. Finally, the quasi-linear constitutive equations are substituted in the balance equations to obtain the field equations. Full article
227 KiB  
Article
On the Darboux Vector of Ruled Surfaces in Pseudo-Galilean Space
by Cumali Ekici and Mustafa Dede
Math. Comput. Appl. 2011, 16(4), 830-838; https://doi.org/10.3390/mca16040830 - 01 Dec 2011
Cited by 1 | Viewed by 1364
Abstract
In the Euclidean space the Darboux vector may be interpreted kinematically as the direction of the instantaneous axis of rotation in the moving trihedron. In this paper we mainly study the Darboux vector of ruled surfaces in pseudo-Galilean space. We obtain relationships between [...] Read more.
In the Euclidean space the Darboux vector may be interpreted kinematically as the direction of the instantaneous axis of rotation in the moving trihedron. In this paper we mainly study the Darboux vector of ruled surfaces in pseudo-Galilean space. We obtain relationships between Darboux and Frenet vectors of each type of ruled surfaces in pseudo-Galilean space. Moreover we observe that in the pseudo-Galilean space the Darboux vector can be interpreted kinematically as a shear along the absolute line. Full article
229 KiB  
Article
Variational Iteration Method for Solving n -th Order Fuzzy Differential Equations
by S. Abbasbandy, T. Allahviranloo, P. Darabi and O. Sedaghatfar
Math. Comput. Appl. 2011, 16(4), 819-829; https://doi.org/10.3390/mca16040819 - 01 Dec 2011
Cited by 6 | Viewed by 1224
Abstract
In this paper, the variational iteration method (VIM) is employed to solve a system of fuzzy differential equations of first order. Since every ordinary fuzzy differential equations of higher order can be converted into a fuzzy system of the first order, this method [...] Read more.
In this paper, the variational iteration method (VIM) is employed to solve a system of fuzzy differential equations of first order. Since every ordinary fuzzy differential equations of higher order can be converted into a fuzzy system of the first order, this method can be used for solving n -th order fuzzy differential equations. Also the convergency of VIM for this system is proved. Finally to more illustrate several examples are solved. Full article
469 KiB  
Article
Energy Efficient Target Tracking with Particle Filtering Techmique in Wireless Sensor Networks
by Aysegul Alaybeyoglu
Math. Comput. Appl. 2011, 16(4), 809-818; https://doi.org/10.3390/mca16040809 - 01 Dec 2011
Viewed by 986
Abstract
In this study, a new target tracking algorithm is proposed for wireless sensor networks. The aim of the algorithm is to decrease energy consumption of the system by decreasing the ratio of target misses. Next location of the target is predicted by using [...] Read more.
In this study, a new target tracking algorithm is proposed for wireless sensor networks. The aim of the algorithm is to decrease energy consumption of the system by decreasing the ratio of target misses. Next location of the target is predicted by using Particle Filtering (PF) technique which aims to represent the posterior density function by a set of random samples with associated weights. Nodes are deployed according to the hexagon shaped network topology in which each of the hexagons represents a cluster with a predetermined leader node. In order to decrease the ratio of target misses, nodes that are closer to the target's predicted location are woken up to make them ready to detect the target. This increases the probability of detecting the target by one of the neighboring hexagons when the target makes sudden turns or unexpected movements. Tracking performance of the proposed algorithm is evaluated by comparing with KNearest Cluster Tracking (KNCT), Wakening Based Target Tracking Algorithm (WBTA)[10] and Generic Static Tracking Approach (GSTA) in terms of miss ratio and energy consumption metrics. Full article
271 KiB  
Article
Application of Energy and Exergy Analyses to a CI Engine Using Biodiesel Fuel
by Perihan Sekmen and Zeki Yılbaşı
Math. Comput. Appl. 2011, 16(4), 797-808; https://doi.org/10.3390/mca16040797 - 01 Dec 2011
Cited by 52 | Viewed by 1786
Abstract
In recent years, exergy analysis method has been widely used in the design, simulation and performance assessment of various types of engines for identifying losses and efficiencies. In this study, the first and second Laws of thermodynamics are employed to analyze the quantity [...] Read more.
In recent years, exergy analysis method has been widely used in the design, simulation and performance assessment of various types of engines for identifying losses and efficiencies. In this study, the first and second Laws of thermodynamics are employed to analyze the quantity and quality of energy in a four-cylinder, direct injection diesel engine using petroleum diesel fuel and biodiesel fuel. The experimental data were collected using steady-state tests which enable accurate measurements of air, fuel and cooling water flow rates, engine load, and all the relevant temperatures. Balances of energy and exergy rates for the engine were determined and then various performance parameters and energy and exergy efficiencies were calculated for each fuel operation and compared with each other. The results of tested biodiesel offer similar energetic performance as petroleum diesel fuel. In addition to this, the exergetic performance parameters usually follow similar trends according to the energetic performance parameters. Full article
304 KiB  
Article
Methods in Mathematica for Solving Ordinary Differential Equations
by Ünal Göktaş and Devendra Kapadia
Math. Comput. Appl. 2011, 16(4), 784-796; https://doi.org/10.3390/mca16040784 - 01 Dec 2011
Cited by 4 | Viewed by 1446
Abstract
An overview of the solution methods for ordinary differential equations in the Mathematica function DSolve is presented. Full article
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