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Ordinary Differential Equations and Applied Dynamics Commons™
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- Global stability (2)
- Homotopy Perturbation Method (2)
- Homotopy perturbation method (2)
- Variational iteration method (2)
- Absorbent term (1)
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- Adomian decomposition method (1)
- Approximate Methods (1)
- Approximate Solution (1)
- Approximate solution (1)
- Automobile (1)
- Caputo derivative (1)
- Computer network (1)
- Descriptor system (1)
- Differential Equation (1)
- Differential Transform Method (1)
- Differential transform method (1)
- Dispersive Long-wave Equations (1)
- Dust-acoustic waves; Hot and cold dust charge; KdV-type equation; Higher order nonlinearity (1)
- Epidemic model (1)
- External force (1)
- Forced oscillation (1)
- Fractional Brownian motion (1)
- Fractional diffusion equation (1)
- Generalized eigenvalues (1)
- Heat flux (1)
- Heat transfer (1)
- Homotopy analysis method (1)
- Hyperbolic equations (1)
- Hyperbolic heat conduction (1)
- Inertia (1)
Articles 1 - 15 of 15
Full-Text Articles in Ordinary Differential Equations and Applied Dynamics
Global Stability Of Worms In Computer Network, Bimal Kumar Mishra, Aditya Kumar Singh
Global Stability Of Worms In Computer Network, Bimal Kumar Mishra, Aditya Kumar Singh
Applications and Applied Mathematics: An International Journal (AAM)
An attempt has been made to show the impact of non-linearity of the worms through SIRS (susceptible – infectious – recovered - susceptible) and SEIRS (susceptible – exposed – infectious – recovered - susceptible) e-epidemic models in computer network. A very general form of non-linear incidence rate has been considered satisfying the worm propagating behavior in computer network. The concavity conditions with a non-linear incidence rate and under the constant population size assumption are shown to be stable. Such systems have either a unique and stable endemic equilibrium state or no endemic equilibrium state at all; in the latter case, …
Solutions Of Nonlinear Second Order Multi-Point Boundary Value Problems By Homotopy Perturbation Method, S. Das, Sunil Kumar, O. P. Singh
Solutions Of Nonlinear Second Order Multi-Point Boundary Value Problems By Homotopy Perturbation Method, S. Das, Sunil Kumar, O. P. Singh
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we present an algorithm for the numerical solution of the second order multi- point boundary value problem with suitable multi boundary conditions. The algorithm is based on the homotopy perturbation approach and the solutions are calculated in the form of a rapid convergent series. It is observed that the method gives more realistic series solutions that converge very rapidly in physical problems. Illustrative numerical examples are provided to demonstrate the efficiency and simplicity of the proposed method in solving this type of multipoint boundary value problems.
On The Eigenvalue And Inertia Problems For Descriptor Systems, Asadollah Aasaraai, Kameleh N. Pirbazari
On The Eigenvalue And Inertia Problems For Descriptor Systems, Asadollah Aasaraai, Kameleh N. Pirbazari
Applications and Applied Mathematics: An International Journal (AAM)
The present study is intended to demonstrate that for a descriptor system with matrix pencil there exists a matrix such that matrix and matrix pencil have the same positive and negative eigenvalues. It is also shown that matrix can be calculated as a contour integral. On the other hand, different representations for matrix are introduced.
Approximate Approach To The Das Model Of Fractional Logistic Population Growth, S. Das, P. K. Gupta, K. Vishal
Approximate Approach To The Das Model Of Fractional Logistic Population Growth, S. Das, P. K. Gupta, K. Vishal
Applications and Applied Mathematics: An International Journal (AAM)
In this article, the analytical method, Homotopy perturbation method (HPM) has been successfully implemented for solving nonlinear logistic model of fractional order. The fractional derivatives are described in the Caputo sense. Using initial value, the explicit solutions of population size for different particular cases have been derived. Numerical results show that the method is extremely efficient to solve this complicated biological model.
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.
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.
Multistage Homotopy Analysis Method For Solving Nonlinear Integral Equations, H. Jafari, M. A. Firoozjaee
Multistage Homotopy Analysis Method For Solving Nonlinear Integral Equations, H. Jafari, M. A. Firoozjaee
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we present an efficient modification of the homotopy analysis method (HAM) that will facilitate the calculations. We then conduct a comparative study between the new modification and the homotopy analysis method. This modification of the homotopy analysis method is applied to nonlinear integral equations and mixed Volterra-Fredholm integral equations, which yields a series solution with accelerated convergence. Numerical illustrations are investigated to show the features of the technique. The modified method accelerates the rapid convergence of the series solution and reduces the size of work.
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.
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.
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.
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.
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.
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.
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 …