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Articles 601 - 630 of 697
Full-Text Articles in Applied Mathematics
Latest Developments In Nonlinear Sciences, Syed T. Mohyud-Din, Ahmet Yildirim
Latest Developments In Nonlinear Sciences, Syed T. Mohyud-Din, Ahmet Yildirim
Applications and Applied Mathematics: An International Journal (AAM)
This paper outlines a detailed study of some latest trends and developments in nonlinear sciences. The major focus of our study will be variational iteration (VIM) and its modifications, homotopy perturbation (HPM), parameter expansion and exp-function methods. The above mentioned schemes are highly accurate, extraordinary efficient, capable to cope with the versatility of the physical problems and are being used to solve a wide class of nonlinear problems. Several examples are given which reveal the justification of our claim.
On Numerical Solutions Of Two-Dimensional Boussinesq Equations By Using Adomian Decomposition And He's Homotopy Perturbation Method, Syed T. Mohyud-Din, Mustafa Inc, Ebru Cavlak
On Numerical Solutions Of Two-Dimensional Boussinesq Equations By Using Adomian Decomposition And He's Homotopy Perturbation Method, Syed T. Mohyud-Din, Mustafa Inc, Ebru Cavlak
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we obtain the approximate solution for 2-dimensional Boussinesq equation with initial condition by Adomian's decomposition and homotopy perturbation methods and numerical results are compared with exact solutions.
Exact Solitary-Wave Special Solutions For The Nonlinear Dispersive K(M,N) Equations By Means Of The Homotopy Analysis Method, Ahmet Yıldırım, Canan Ünlü, Syed T. Mohyud-Din
Exact Solitary-Wave Special Solutions For The Nonlinear Dispersive K(M,N) Equations By Means Of The Homotopy Analysis Method, Ahmet Yıldırım, Canan Ünlü, Syed T. Mohyud-Din
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we study the nonlinear dispersive K(m,n) equations which exhibit solutions with solitary patterns. New exact solitary solutions are found. The two special cases, K(2, 2) and K(3, 3), are chosen to illustrate the concrete features of the homotopy analysis method in K(m,n) equations. The nonlinear equations K(m,n) are studied for two different cases, namely when m = n being odd and even integers. General formulas for the solutions of K(m,n) equations are established.
A Note On He’S Parameter-Expansion Method Of Coupled Van Der Pol–Duffing Oscillators, N. H. Sweilam, M. M. Khader
A Note On He’S Parameter-Expansion Method Of Coupled Van Der Pol–Duffing Oscillators, N. H. Sweilam, M. M. Khader
Applications and Applied Mathematics: An International Journal (AAM)
This paper presents the analytical and approximate solutions of the coupled chaotic Van der Pol-Duffing systems, by using the He's parameter-expansion method (PEM). One iteration is sufficient to obtain a highly accurate solution, which is valid for the whole solution domain. From the obtained results, we can conclude that the suggest method, is of utter simplicity, and can be easily extended to all kinds of non-linear equations.
Modified Variational Iteration Method For Second Order Initial Value Problems, Fazhan Geng
Modified Variational Iteration Method For Second Order Initial Value Problems, Fazhan Geng
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we introduce a modified variational iteration method for second order initial value problems by transforming the integral of iteration process. The main advantages of this modification are that it can overcome the restriction of the form of nonlinearity term in differential equations and improve the iterative speed of conventional variational iteration method. The method is applied to some nonlinear second order initial value problems and the numerical results reveal that the modified method is accurate and efficient for second order initial value problems.
Forced Oscillations Of Nonlinear Hyperbolic Equations With Functional Arguments Via Riccati Method, Yutaka Shoukaku
Forced Oscillations Of Nonlinear Hyperbolic Equations With Functional Arguments Via Riccati Method, Yutaka Shoukaku
Applications and Applied Mathematics: An International Journal (AAM)
By using integral averaging method and a generalized Riccati technique, sufficient conditions are established for the oscillation of solutions of forced nonlinear hyperbolic equations with functional arguments.
Homotopy Perturbation Method And The Stagnation Point Flow, P. Donald Ariel
Homotopy Perturbation Method And The Stagnation Point Flow, P. Donald Ariel
Applications and Applied Mathematics: An International Journal (AAM)
The laminar steady flow of an incompressible, viscous fluid near a stagnation point has been computed using the homotopy perturbation method (HPM). Both the cases, (i) two-dimensional flow and (ii) axisymmetric flow, have been considered. A sequence of successive approximations has been obtained in the solution, and the convergence of the sequence is achieved by using the Padé approximants. It is found that there is a complete agreement between the results obtained by the HPM and the exact numerical solution.
The He's Variational Iteration Method For Solving The Integro-Differential Parabolic Problem With Integral Conditions, Saeid Abbasbandy, Hadi R. Ghehsareh
The He's Variational Iteration Method For Solving The Integro-Differential Parabolic Problem With Integral Conditions, Saeid Abbasbandy, Hadi R. Ghehsareh
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, the variational iteration method is applied for finding the solution of an Integro-differential parabolic problem with integral conditions. Convergence of the proposed method is also discussed. Finally, some numerical examples are given to show the effectiveness of the proposed method.
Revised Variational Iteration Method For Solving Systems Of Ordinary Differential Equations, Elham Salehpoor, Hossein Jafari, Merieh A. Afrapoli
Revised Variational Iteration Method For Solving Systems Of Ordinary Differential Equations, Elham Salehpoor, Hossein Jafari, Merieh A. Afrapoli
Applications and Applied Mathematics: An International Journal (AAM)
A modification of the variational iteration method applied to systems of linear/non-linear ordinary differential equations, which yields a series solution with accelerated convergence, has been presented. Illustrative examples have been given.
An Approximate Analytical Solution Of The Fractional Diffusion Equation With External Force And Different Type Of Absorbent Term - Revisited, S. Das, R. Kumar, P. K. Gupta
An Approximate Analytical Solution Of The Fractional Diffusion Equation With External Force And Different Type Of Absorbent Term - Revisited, S. Das, R. Kumar, P. K. Gupta
Applications and Applied Mathematics: An International Journal (AAM)
In this article Homotopy Perturbation Method (HPM) is applied to obtain an approximate analytical solution of a fractional diffusion equation with an external force and a reaction term different from the reaction term used by Das and Gupta (2010). The anomalous behavior of diffusivity in presence or absence of linear external force due to the presence of this force of reaction term are obtained and presented graphically.
Solutions Of Tenth And Ninth-Order Boundary Value Problems By Modified Variational Iteration Method, Syed Tauseef Mohyud-Din, Ahmet Yildirim
Solutions Of Tenth And Ninth-Order Boundary Value Problems By Modified Variational Iteration Method, Syed Tauseef Mohyud-Din, Ahmet Yildirim
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we apply the modified variational iteration method (MVIM) for solving the ninth and tenth-order boundary value problems. The proposed modification is made by introducing He’s polynomials in the correction functional. The suggested algorithm is quite efficient and is practically well suited for use in these problems. The proposed iterative scheme finds the solution without any discretization, linearization or restrictive assumptions. Several examples are given to verify the reliability and efficiency of the method. The fact that the proposed technique solves nonlinear problems without using the Adomian’s polynomials can be considered as a clear advantage of this algorithm …
A Resource Based Stage-Structured Fishery Model With Selective Harvesting Of Mature Species, T. K. Kar, Swarnakamal Misra
A Resource Based Stage-Structured Fishery Model With Selective Harvesting Of Mature Species, T. K. Kar, Swarnakamal Misra
Applications and Applied Mathematics: An International Journal (AAM)
In this paper we have considered a model in which revenue is generated from fishing and the growth of the fish depends upon the plankton which in turn follows a logistic law of growth. Here the fish population has two stages, a juvenile stage and a mature stage and we consider the harvesting of the mature fish species. Stability and permanence of the system are discussed. Maximum sustainable yield, maximum economic yield and optimal sustainable yield are obtained and different tax policies are discussed to achieve the reference points.
Application Of Homotopy Analysis Method To Fourth-Order Parabolic Partial Differential Equations, M. Matinfar, M. Saeidy
Application Of Homotopy Analysis Method To Fourth-Order Parabolic Partial Differential Equations, M. Matinfar, M. Saeidy
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, by means of the homotopy analysis method (HAM), the solutions of some fourthorder parabolic partial differential equations are exactly obtained in the form of convergent Taylor series. The HAM contains the auxiliary parameter h that provides a convenient way of controlling the convergent region of series solutions. This analytical method is employed to solve linear examples to obtain the exact solutions. The results reveal that the proposed method is very effective and simple.
Bianchi Type I Bulk Viscous Fluid String Dust Cosmological Model With Magnetic Field In Bimetric Theory Of Gravitation, M. S. Borkar, S. S. Charjan
Bianchi Type I Bulk Viscous Fluid String Dust Cosmological Model With Magnetic Field In Bimetric Theory Of Gravitation, M. S. Borkar, S. S. Charjan
Applications and Applied Mathematics: An International Journal (AAM)
In the presence of both magnetic field and bulk viscosity, Bianchi Type I bulk viscous fluid string dust cosmological model in Rosen’s bimetric theory of gravitation have been investigated by using the technique of Letelier and Stachel. The nature of the model is discussed in the absence of both magnetic field and bulk viscosity. To get a determinate solution, we have assumed the condition that σ is proportional to θ and ζθ = constant where σ is the shear, θ is the expansion in the model and ζ is the coefficient of bulk viscosity. Further the physical and geometrical significance …
Wavelet Transform Of Fractional Integrals For Integrable Boehmians, Deshna Loonker, P. K. Banerji, S. L. Kalla
Wavelet Transform Of Fractional Integrals For Integrable Boehmians, Deshna Loonker, P. K. Banerji, S. L. Kalla
Applications and Applied Mathematics: An International Journal (AAM)
The present paper deals with the wavelet transform of fractional integral operator (the Riemann- Liouville operators) on Boehmian spaces. By virtue of the existing relation between the wavelet transform and the Fourier transform, we obtained integrable Boehmians defined on the Boehmian space for the wavelet transform of fractional integrals.
Comparison Differential Transformation Technique With Adomian Decomposition Method For Dispersive Long-Wave Equations In (2+1)-Dimensions, M. A. Mohamed
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we will introduce two methods to obtain the numerical solutions for the system of dispersive long-wave equations (DLWE) in (2+1)-dimensions. The first method is the differential transformation method (DTM) and the second method is Adomian decomposition method (ADM). Moreover, we will make comparison between the solutions obtained by the two methods. Consequently, the results of our system tell us the two methods can be alternative ways for solution of the linear and nonlinear higher-order initial value problems.
Developing An Improved Shift-And-Invert Arnoldi Method, H. Saberi Najafi, M. Shams Solary
Developing An Improved Shift-And-Invert Arnoldi Method, H. Saberi Najafi, M. Shams Solary
Applications and Applied Mathematics: An International Journal (AAM)
An algorithm has been developed for finding a number of eigenvalues close to a given shift and in interval [ Lb,Ub ] of a large unsymmetric matrix pair. The algorithm is based on the shift-andinvert Arnoldi with a block matrix method. The block matrix method is simple and it uses for obtaining the inverse matrix. This algorithm also accelerates the shift-and-invert Arnoldi Algorithm by selecting a suitable shift. We call this algorithm Block Shift-and-Invert or BSI. Numerical examples are presented and a comparison has been shown with the results obtained by Sptarn Algorithm in Matlab. The results show that the …
Improved Dust Acoustic Solitary Waves In Two Temperature Dust Fluids, E. K. El-Shewy, H. G. Abdelwahed, M. I. Abo El Maaty, M. A. Elmessary
Improved Dust Acoustic Solitary Waves In Two Temperature Dust Fluids, E. K. El-Shewy, H. G. Abdelwahed, M. I. Abo El Maaty, M. A. Elmessary
Applications and Applied Mathematics: An International Journal (AAM)
A theoretical investigation is carried out for contribution of the higher-order nonlinearity to nonlinear dust-acoustic solitary waves (DASWs) in an unmagnetized two types of dust fluids (one cold and the other is hot) in the presence of Bolltzmannian ions and electrons. A KdV equation that contains the lowest-order nonlinearity and dispersion is derived from the lowest order of perturbation and a linear inhomogeneous (KdV-type) equation that accounts for the higher-order nonlinearity and dispersion is obtained. A stationary solution for equations resulting from higher-order perturbation theory has been found using the renormalization method. The effects of hot and cold dust charge …
Variational Iteration Method For Solving Two-Parameter Singularly Perturbed Two Point Boundary Value Problem, Marwan Taiseer Alquran, Nurettin Doğan
Variational Iteration Method For Solving Two-Parameter Singularly Perturbed Two Point Boundary Value Problem, Marwan Taiseer Alquran, Nurettin Doğan
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, He’s Variational iteration method (VIM) is used for the solution of singularly perturbed two-point boundary value problems with two small parameters multiplying the derivatives. Some problems are solved to demonstrate the applicability of the method. This paper suggests a patern for choosing the freely selected initial approximation in the VIM that leads to a very well approximation by only one iteration.
Convergence Of The Sinc Method Applied To Volterra Integral Equations, M. Zarebnia, J. Rashidinia
Convergence Of The Sinc Method Applied To Volterra Integral Equations, M. Zarebnia, J. Rashidinia
Applications and Applied Mathematics: An International Journal (AAM)
A collocation procedure is developed for the linear and nonlinear Volterra integral equations, using the globally defined Sinc and auxiliary basis functions. We analytically show the exponential convergence of the Sinc collocation method for approximate solution of Volterra integral equations. Numerical examples are included to confirm applicability and justify rapid convergence of our method.
Inverse Heat Conduction Problem In A Semi-Infinite Circular Plate And Its Thermal Deflection By Quasi-Static Approach, K. C. Deshmukh, S. C. Warbhe, G. D. Kedar, V. S. Kulkarni
Inverse Heat Conduction Problem In A Semi-Infinite Circular Plate And Its Thermal Deflection By Quasi-Static Approach, K. C. Deshmukh, S. C. Warbhe, G. D. Kedar, V. S. Kulkarni
Applications and Applied Mathematics: An International Journal (AAM)
This paper concerns the inverse heat conduction problem in a semi-infinite thin circular plate subjected to an arbitrary known temperature under unsteady condition and the behavior of thermal deflection has been discussed on the outer curved surface with the help of mathematical modeling. The solutions are obtained in an analytical form by using the integral transform technique.
Approximations Of Sturm-Liouville Eigenvalues Using Sinc-Galerkin And Differential Transform Methods, Marwan Taiseer Alquran, Kamel Al-Khaled
Approximations Of Sturm-Liouville Eigenvalues Using Sinc-Galerkin And Differential Transform Methods, Marwan Taiseer Alquran, Kamel Al-Khaled
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we present a comparative study of Sinc-Galerkin method and differential transform method to solve Sturm-Liouville eigenvalue problem. As an application, a comparison between the two methods for various celebrated Sturm-Liouville problems are analyzed for their eigenvalues and solutions. The study outlines the significant features of the two methods. The results show that these methods are very efficient, and can be applied to a large class of problems. The comparison of the methods shows that although the numerical results of these methods are the same, differential transform method is much easier, and more efficient than the Sinc-Galerkin method.
Soliton And Periodic Solutions For (3+1)-Dimensional Nonlinear Evolution Equations By Exp-Function Method, A. Borhanifar, M. M. Kabir
Soliton And Periodic Solutions For (3+1)-Dimensional Nonlinear Evolution Equations By Exp-Function Method, A. Borhanifar, M. M. Kabir
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, (3+1)-dimensional Jimbo-Miwa and (3+1)-dimensional potential-YTSF equations are considered and the Exp-Function method is employed to compute the exact solutions. The solutions obtained by this method are compared with the exact solutions obtained through other methods. These equations play a very important role in mathematical physics and engineering sciences. It is shown that the Exp-Function method, with the help of symbolic computation, provides a powerful mathematical tool for solving nonlinear evolution equations in mathematical physics
Effects Of Radiation And Variable Viscosity On Mhd Free Convective Flow And Mass Transfer Over A Stretching Sheet With Chemical Reaction, M. A. Seddeek, A. A. Almushigeh
Effects Of Radiation And Variable Viscosity On Mhd Free Convective Flow And Mass Transfer Over A Stretching Sheet With Chemical Reaction, M. A. Seddeek, A. A. Almushigeh
Applications and Applied Mathematics: An International Journal (AAM)
A similarity solution is proposed for the analysis of steady free convection heat and mass transfer over a stretching sheet. The effect of radiation, chemical reaction and variable viscosity on hydromagnetic heat and mass transfer in the presence of magnetic field are investigated. The governing partial differential equations are transformed to the ordinary differential equations using similarity variables, and then solved numerically by means of the fourth-order Runge– Kutta method with shooting technique. A comparison with exact solution is performed and the results are found to be in excellent. Numerical results for the velocity, temperature and concentration as well as …
Temperature Profiles In A Disc Brake, K. Venkateswara Reddy, D. Rama Murthy
Temperature Profiles In A Disc Brake, K. Venkateswara Reddy, D. Rama Murthy
Applications and Applied Mathematics: An International Journal (AAM)
The Science of heat transfer allows us to determine the time rate of energy transfer caused by non equilibrium of temperatures. The importance of heat transfer in proper design of Automobiles has long been recognized. In this paper we determined the transient temperature distributions in a disc brake during a single brake application using Finite difference numerical technique. Hyperbolic heat conduction which includes the effect of the finite heat propagation is gaining importance. It is necessary to consider hyperbolic heat conduction in problems involving short time intervals and for very high heat fluxes. Here we considered both parabolic and hyperbolic …
A Generalized Newton-Penalty Algorithm For Large Scale Ill-Conditioned Quadratic Problems, Maziar Salahi, Moslem Ganji
A Generalized Newton-Penalty Algorithm For Large Scale Ill-Conditioned Quadratic Problems, Maziar Salahi, Moslem Ganji
Applications and Applied Mathematics: An International Journal (AAM)
Large scale quadratic problems arise in many real world applications. It is quite often that the coefficient matrices in these problems are ill-conditioned. Thus, if the problem data are available even with small error, then solving them using classical algorithms might result to meaningless solutions. In this short paper, we propose an efficient generalized Newton-penalty algorithm for solving these problems. Our computational results show that our new simple algorithm is much faster and better than the approach of Rojas et al. (2000), which requires parameter tuning for different problems.
Higher Order Difference Schemes For Heat Equation, Jianzhong Wang
Higher Order Difference Schemes For Heat Equation, Jianzhong Wang
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we construct the explicit difference schemes for the heat equation with arbitrary high orders. We also show the validity of the new schemes by numerical simulations.
Remarks On The Stability Of Some Size-Structured Population Models V: The Case When The Death Rate Depends On Adults Only And The Growth Rate Depends On Size Only, M. El-Doma
Applications and Applied Mathematics: An International Journal (AAM)
We continue our study of size-structured population dynamics models when the population is divided into adults and juveniles, started in El-Doma (To appear). We concentrate our efforts in the special case when the death rate depends on adults only, the growth rate depends on size only and the maximum size for an individual in the population is infinite. Three demographic parameters are identified and are shown to determine conditions for the (in)stability of a nontrivial steady state. We also give examples that illustrate the stability results. The results in this paper generalize previous results, for example, see Calsina, et al. …
Some Applications Of The (G'/G)-Expansion Method For Solving The Nonlinear Partial Differential Equations In Mathematical Physics, Nasir Taghizade, Ahmad Neirameh
Some Applications Of The (G'/G)-Expansion Method For Solving The Nonlinear Partial Differential Equations In Mathematical Physics, Nasir Taghizade, Ahmad Neirameh
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we construct the traveling wave solutions involving parameters of the combined Kdv-MKdv equation, the Shorma-Tasso-Olver equation and (2+1)-dimensional Konopelchenko-Dubrovsky equation, by using a new approach method. When the parameters are taken special values, the solitary waves are derived from the traveling waves. The travelling wave solutions are expressed by the hyperbolic functions, the trigonometric functions and the rational functions.
Uniform Stabilization Of N-Dimensional Vibrating Equation Modeling ‘Standard Linear Model’ Of Viscoelasticity, Ganesh C. Gorain
Uniform Stabilization Of N-Dimensional Vibrating Equation Modeling ‘Standard Linear Model’ Of Viscoelasticity, Ganesh C. Gorain
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we deal with the elastic vibrations of flexible structures modeled by the ‘standard linear model’ of viscoelasticity in n-dimensional space. We study the uniform exponential stabilization of such kind of vibrations after incorporating separately very small amount of passive viscous damping and internal material damping of Kelvin-Viogt type in the model. Explicit forms of exponential energy decay rates are obtained by a direct method, for the solution of such boundary value problems without having to introduce any boundary feedback.