Open Access. Powered by Scholars. Published by Universities.®
Ordinary Differential Equations and Applied Dynamics Commons™
Open Access. Powered by Scholars. Published by Universities.®
- Keyword
-
- Ecliptic Plane (2)
- Fractional calculus (2)
- Inhomogeneity (2)
- MHD (2)
- Poynting-Robertson drag (2)
-
- Resonance (2)
- Thermal Stresses (2)
- Three-body problem (2)
- Approximate Solution (1)
- Aqueous humor (1)
- Bagley-Torvik Equation (1)
- Bernoulli sub-ODE method (1)
- Bernstein polynomials (1)
- Blasius equation (1)
- Boundary layer flow (1)
- Boundedness (1)
- Caputo derivative (1)
- Chemical reaction (1)
- Conformable fractional derivative (1)
- Convection (1)
- Differential Equation (1)
- Differential equations (1)
- Direct algebraic method (1)
- Dissipation (1)
- Dust-acoustic waves (1)
- Effect of Oblateness (1)
- Electron acoustic waves; pseudo-potential; reductive perturbation; Symbolic computations; explosive solutions. (1)
- Elliptic Cylinder (1)
- Elliptical coordinates (1)
- Exp-function method (1)
Articles 1 - 21 of 21
Full-Text Articles in Ordinary Differential Equations and Applied Dynamics
Exact Solutions Of Two Nonlinear Space-Time Fractional Differential Equations By Application Of Exp-Function Method, Elahe M. Eskandari, Nasir Taghizadeh
Exact Solutions Of Two Nonlinear Space-Time Fractional Differential Equations By Application Of Exp-Function Method, Elahe M. Eskandari, Nasir Taghizadeh
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we discuss on the exact solutions of the nonlinear space-time fractional Burgerlike equation and also the nonlinear fractional fifth-order Sawada-Kotera equation with the expfunction method.We use the functional derivatives in the sense of Riemann-Jumarie derivative and fractional convenient variable transformation in this study. Further, we obtain some exact analytical solutions including hyperbolic function.
Generalized Bagley-Torvik Equation And Fractional Oscillators, Mark Naber, Lucas Lymburner
Generalized Bagley-Torvik Equation And Fractional Oscillators, Mark Naber, Lucas Lymburner
Applications and Applied Mathematics: An International Journal (AAM)
In this paper the Bagley-Torvik Equation is considered with the order of the damping term allowed to range between one and two. The solution is found to be representable as a convolution of trigonometric and exponential functions with the driving force. The properties of the effective decay rate and the oscillation frequency with respect to the order of the fractional damping are also studied. It is found that the effective decay rate and oscillation frequency have a complex dependency on the order of the derivative of the damping term and exhibit properties one might expect of a thermodynamic Equation of …
Resonance In The Motion Of A Geocentric Satellite Due To Poynting-Robertson Drag And Equatorial Ellipticity Of The Earth, Charanpreet Kaur, Binay K. Sharma, Sushil Yadav
Resonance In The Motion Of A Geocentric Satellite Due To Poynting-Robertson Drag And Equatorial Ellipticity Of The Earth, Charanpreet Kaur, Binay K. Sharma, Sushil Yadav
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, the problem of resonance in a motion of a geocentric satellite is numerically investigated under the consolidated gravitational forces of the Sun, the Earth including Earth’s equatorial ellipticity parameter and Poynting-Robertson (P-R) drag. We are presuming that bodies lying on an ecliptic plane are the Sun and the Earth, and satellite on orbital plane. Resonance is monitored between satellite’s mean motion and average angular velocity of the Earth around the Sun, and also between satellite’s mean motion and equatorial ellipticity parameter of the Earth. We also perform a systematic and thorough analysis in an attempt to understand …
Thermoelastic Stress Analysis Of A Functionally Graded Transversely Isotropic Hollow Cylinder In Elliptical Coordinates, Tara Dhakate, Vinod Varghese, Lalsingh Khalsa
Thermoelastic Stress Analysis Of A Functionally Graded Transversely Isotropic Hollow Cylinder In Elliptical Coordinates, Tara Dhakate, Vinod Varghese, Lalsingh Khalsa
Applications and Applied Mathematics: An International Journal (AAM)
This paper is concerned with the axisymmetric thermoelastic problem to investigate the influence of nonlinear heat conduction equation, displacement functions and thermal stresses of a functionally graded transversely isotropic hollow cylinder that is presented in the elliptical coordinate system. The method of integral transform technique is used to produce an exact solution of the heat conduction equation in which sources are generated according to a linear function of the temperature. An explicit exact solution of the governing thermoelastic equation is proposed when material properties are power-law functions with the exponential form of the radial coordinate. Numerical calculations are also carried …
Resonance In The Motion Of A Geocentric Satellite Due To Poynting-Robertson Drag, Charanpreet Kaur, Binay K. Sharma, L. P. Pandey
Resonance In The Motion Of A Geocentric Satellite Due To Poynting-Robertson Drag, Charanpreet Kaur, Binay K. Sharma, L. P. Pandey
Applications and Applied Mathematics: An International Journal (AAM)
The problem of resonance in a geocentric Satellite under the combined gravitational forces of the Sun and the Earth due to Poynting-Robertson (P-R) drag has been discussed in this paper with the assumption that all three bodies, the Earth, the Sun and the Satellite, lie in an ecliptic plane. Our approach differs from conventional ones as we have placed evaluated velocity of the Satellite in equations of motion.We observed five resonance points commensurable between the mean motion of the Satellite and the average angular velocity of the Earth around the Sun, out of which two resonances occur only due to …
Thermoelastic Analysis Of A Nonhomogeneous Hollow Cylinder With Internal Heat Generation, V. R. Manthena, N. K. Lamba, G. D. Kedar
Thermoelastic Analysis Of A Nonhomogeneous Hollow Cylinder With Internal Heat Generation, V. R. Manthena, N. K. Lamba, G. D. Kedar
Applications and Applied Mathematics: An International Journal (AAM)
In the present paper, we have determined the heat conduction and thermal stresses of a hollow cylinder with inhomogeneous material properties and internal heat generation. All the material properties except Poisson’s ratio and density are assumed to be given by a simple power law in axial direction. We have obtained the solution of the two dimensional heat conduction equation in the transient state in terms of Bessel’s and trigonometric functions. The influence of inhomogeneity on the thermal and mechanical behavior is examined. Numerical computations are carried out for both homogeneous and nonhomogeneous cylinders and are represented graphically.
Thermal Stress Analysis In A Functionally Graded Hollow Elliptic-Cylinder Subjected To Uniform Temperature Distribution, V. R. Manthena, N. K. Lamba, G. D. Kedar
Thermal Stress Analysis In A Functionally Graded Hollow Elliptic-Cylinder Subjected To Uniform Temperature Distribution, V. R. Manthena, N. K. Lamba, G. D. Kedar
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, an analytical method of a thermoelastic problem for a medium with functionally graded material properties is developed in a theoretical manner for the elliptic-cylindrical coordinate system under the assumption that the material properties except for Poisson’s ratio and density are assumed to vary arbitrarily with the exponential law in the radial direction. An attempt has been made to reconsider the fundamental system of equations for functionally graded solids in a two-dimensional state under thermal and mechanical loads. The general solution of displacement formulation is obtained by the introduction of appropriate transformation and carried out the analysis by …
Numerical Solution Of Fractional Integro-Differential Equations With Nonlocal Conditions, M. Jani, D. Bhatta, S. Javadi
Numerical Solution Of Fractional Integro-Differential Equations With Nonlocal Conditions, M. Jani, D. Bhatta, S. Javadi
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we present a numerical method for solving fractional integro-differential equations with nonlocal boundary conditions using Bernstein polynomials. Some theoretical considerations regarding fractional order derivatives of Bernstein polynomials are discussed. The error analysis is carried out and supported with some numerical examples. It is shown that the method is simple and accurate for the given problem.
Effect Of Nonlinear Thermal Radiation On Mhd Chemically Reacting Maxwell Fluid Flow Past A Linearly Stretching Sheet, A. M. Ramireddy, J. V. Ramana Reddy, N. Sandeep, V. Sugunamma
Effect Of Nonlinear Thermal Radiation On Mhd Chemically Reacting Maxwell Fluid Flow Past A Linearly Stretching Sheet, A. M. Ramireddy, J. V. Ramana Reddy, N. Sandeep, V. Sugunamma
Applications and Applied Mathematics: An International Journal (AAM)
This communication addresses the influence of nonlinear thermal radiation on magneto hydrodynamic Maxwell fluid flow past a linearly stretching surface with heat and mass transfer. The effects of heat generation/absorption and chemical reaction are taken into account. At first, we converted the governing partial differential equations into nonlinear ordinary differential equations with the help of suitable similarity transformations and solved by using Runge-Kutta based shooting technique. Further, the effects of various physical parameters on velocity, temperature and concentration fields were discussed thoroughly with the help of graphs obtained by using bvp5c MATLAB package. In view of many engineering applications we …
New Structure For Exact Solutions Of Nonlinear Time Fractional Sharma-Tasso-Olver Equation Via Conformable Fractional Derivative, Hadi Rezazadeh, Farid S. Khodadad, Jalil Manafian
New Structure For Exact Solutions Of Nonlinear Time Fractional Sharma-Tasso-Olver Equation Via Conformable Fractional Derivative, Hadi Rezazadeh, Farid S. Khodadad, Jalil Manafian
Applications and Applied Mathematics: An International Journal (AAM)
In this paper new fractional derivative and direct algebraic method are used to construct exact solutions of the nonlinear time fractional Sharma-Tasso-Olver equation. As a result, three families of exact analytical solutions are obtained. The results reveal that the proposed method is very effective and simple for obtaining approximate solutions of nonlinear fractional partial differential equations.
Numerical Simulation Of The Phase Space Of Jupiter-Europa System Including The Effect Of Oblateness, Vinay Kumar, Beena R. Gupta, Rajiv Aggarwal
Numerical Simulation Of The Phase Space Of Jupiter-Europa System Including The Effect Of Oblateness, Vinay Kumar, Beena R. Gupta, Rajiv Aggarwal
Applications and Applied Mathematics: An International Journal (AAM)
We have numerically investigated the phase space of the Jupiter-Europa system in the framework of a Circular Restricted Three-Body Problem. In our model, Jupiter is taken as oblate primary. We have considered time-frequency analysis (TFA) based on wavelets and the Poincare Surface of Section (PSS) for the characterization of orbits in the Jupiter-Europa model. We have exploited both cases: a system with and without considering the effect of oblateness. Graphs (ridge-plots) explaining the phenomenon of resonance trapping, a difference between chaotic sticky orbit and the non-sticky orbit, and periodic and quasi-periodic orbit are presented. Our results of Poincare surfaces of …
Complex Solutions Of The Time Fractional Gross-Pitaevskii (Gp) Equation With External Potential By Using A Reliable Method, Nasir Taghizadeh, Mona N. Foumani
Complex Solutions Of The Time Fractional Gross-Pitaevskii (Gp) Equation With External Potential By Using A Reliable Method, Nasir Taghizadeh, Mona N. Foumani
Applications and Applied Mathematics: An International Journal (AAM)
In this article, modified (G'/G )-expansion method is presented to establish the exact complex solutions of the time fractional Gross-Pitaevskii (GP) equation in the sense of the conformable fractional derivative. This method is an effective method in finding exact traveling wave solutions of nonlinear evolution equations (NLEEs) in mathematical physics. The present approach has the potential to be applied to other nonlinear fractional differential equations. Based on two transformations, fractional GP equation can be converted into nonlinear ordinary differential equation of integer orders. In the end, we will discuss the solutions of the fractional GP equation with external potentials.
On The Global Existence And Boundedness Of Solutions Of Nonlinear Vector Differential Equations Of Third Order, Timur Ayhan, Cemil Tunç
On The Global Existence And Boundedness Of Solutions Of Nonlinear Vector Differential Equations Of Third Order, Timur Ayhan, Cemil Tunç
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we give some criteria to ensure the global existence and boundedness of solutions to a kind of third order nonlinear vector differential equations. By using the Lyapunov's direct method, we obtain a new result on the topic and give an example for the illustrations. Our result includes, completes and improves some earlier results in the literature.
New Exact Solutions Of The Perturbed Nonlinear Fractional Schr¨Odinger Equation Using Two Reliable Methods, Nasir Taghizadeh, Mona N. Foumani, Vahid S. Mohammadi
New Exact Solutions Of The Perturbed Nonlinear Fractional Schr¨Odinger Equation Using Two Reliable Methods, Nasir Taghizadeh, Mona N. Foumani, Vahid S. Mohammadi
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, the fractional derivatives in the sense of the modified Riemann-Liouville derivative and the first integral method and the Bernoulli sub-ODE method are employed for constructing the exact complex solutions of the perturbed nonlinear fractional Schr ¨odinger equation and comparing the solutions.
A Hybrid Variational Iteration Method For Blasius Equation, M. Sajid, N. Ali, T. Javed
A Hybrid Variational Iteration Method For Blasius Equation, M. Sajid, N. Ali, T. Javed
Applications and Applied Mathematics: An International Journal (AAM)
The objective of this paper is to present the hybrid variational iteration method. The proposed algorithm is based on the combination of variational iteration and shooting methods. In the proposed algorithm the entire domain is divided into subintervals to establish the accuracy and convergence of the approximate solution. It is found that in each subinterval a three term approximate solution using variational iteration method is sufficient. The proposed hybrid variational iteration method offers not only numerical values, but also closed form analytic solutions in each subinterval. The method is implemented using an example of the Blasius equation. The results show …
Unsteady Boundary Layer Flow Of Thermophoretic Mhd Nanofluid Past A Stretching Sheet With Space And Time Dependent Internal Heat Source/Sink, N. Sandeep, C. Sulochana, C. S. K. Raju, M. J. Babu, V. Sugunamma
Unsteady Boundary Layer Flow Of Thermophoretic Mhd Nanofluid Past A Stretching Sheet With Space And Time Dependent Internal Heat Source/Sink, N. Sandeep, C. Sulochana, C. S. K. Raju, M. J. Babu, V. Sugunamma
Applications and Applied Mathematics: An International Journal (AAM)
In this study we analyze the boundary layer flow of a thermophoretic magnetohydrodynamic dissipative nanofluid over an unsteady stretching sheet in a porous medium with space and time dependent internal heat source/sink. The governing equations are transformed to ordinary differential equations by using similarity transformation. Numerical solutions of these equations are obtained by using the Shooting Technique. The effects of non-dimensional governing parameters on the velocity, temperature, concentration profiles, friction factor, Nusselt and Sherwood numbers are discussed and presented through graphs and tables. Accuracy of the results compared with the existing ones. Excellent agreement is found with earlier studies.
Scaling Group Analysis On Mhd Free Convective Heat And Mass Transfer Over A Stretching Surface With Suction / Injection, Heat Source/Sink Considering Viscous Dissipation And Chemical Reaction Effects, Hunegnaw Dessie, Naikoti Kishan
Scaling Group Analysis On Mhd Free Convective Heat And Mass Transfer Over A Stretching Surface With Suction / Injection, Heat Source/Sink Considering Viscous Dissipation And Chemical Reaction Effects, Hunegnaw Dessie, Naikoti Kishan
Applications and Applied Mathematics: An International Journal (AAM)
This paper concerns with scaling group analysis on MHD free convective heat and mass transfer over stretching surface considering effects of thermal-diffusion and diffusion-thermo with suction /injection, heat source/sink and chemical reaction by taking into account viscous dissipation. Scaling group transformations are used to convert the partial differential equations of governing equations into ordinary differential equation and are solved numerically by Keller Box Method. Numerical results obtained for different parameters are drawn graphically and their effects on velocity, temperature and concentration profiles are discussed and shown graphically. Skin-friction coefficient, Nusselt number and Sherwood number are presented in table. It is …
Modelling The Flow Of Aqueous Humor In Schlemm’S Canal In The Eye, Ram Avtar, Swati Srivastava, Rashmi Srivastava
Modelling The Flow Of Aqueous Humor In Schlemm’S Canal In The Eye, Ram Avtar, Swati Srivastava, Rashmi Srivastava
Applications and Applied Mathematics: An International Journal (AAM)
A simple mathematical model for the transient flow of aqueous humor in the canal of Schlemm is developed to investigate the acceleration effects of a sudden elevation in the intraocular pressure on the flow characteristics of the aqueous humor in the canal. The model treats a canal segment as a tube of elliptic cross-section. Exact analytical solution to the model is obtained using separation of variables method. The effects of some important model parameters on the maximum and minimum shear stresses exerted on the Schlemm’s canal epithelial cells (wall) by flowing aqueous humor are investigated for the steady-state flow.
Solitary, Explosive, Rational And Elliptic Doubly Periodic Solutions For Nonlinear Electron-Acoustic Waves In The Earth’S Magnetotail Region With Cold Electron Fluid And Isothermal Ions, S. A. El-Wakil, E. M. Abulwafa, M. A. Abdou, E. K. El-Shewy, H. M. Abd-El-Hamid
Solitary, Explosive, Rational And Elliptic Doubly Periodic Solutions For Nonlinear Electron-Acoustic Waves In The Earth’S Magnetotail Region With Cold Electron Fluid And Isothermal Ions, S. A. El-Wakil, E. M. Abulwafa, M. A. Abdou, E. K. El-Shewy, H. M. Abd-El-Hamid
Applications and Applied Mathematics: An International Journal (AAM)
A theoretical investigation has been made of electron acoustic wave propagating in unmagnetized collisionless plasma consisting of a cold electron fluid and isothermal ions with two different temperatures obeying Boltzmann type distributions. Based on the pseudo-potential approach, large amplitude potential structures and the existence of Solitary waves are discussed. The reductive perturbation method has been employed to derive the Korteweg-de Vries equation for small but finite amplitude electrostatic waves. An algebraic method with computerized symbolic computation, which greatly exceeds the applicability of the existing tanh, extended tanh methods in obtaining a series of exact solutions of the KdV equation, is …
Dust-Acoustic Solitary Waves In Magnetized Dusty Plasma With Dust Opposite Polarity, S. A. El-Wakil, M. T. Attia, E. K. El-Shewy, S. K. Zaghbeer, H. G. Abdelwahed
Dust-Acoustic Solitary Waves In Magnetized Dusty Plasma With Dust Opposite Polarity, S. A. El-Wakil, M. T. Attia, E. K. El-Shewy, S. K. Zaghbeer, H. G. Abdelwahed
Applications and Applied Mathematics: An International Journal (AAM)
The nonlinear propagation of small but finite amplitude dust-acoustic solitary waves (DAWs) in magnetized collision less dusty plasma has been investigated. The fluid model is a four component magnetized dusty plasma, consisting of positive and negative dust species, isothermal electrons and ions in the presence of an external magnetic field. A reductive perturbation method was employed to obtain the Zakharov Kuznetsov (ZK) equation for the first-order potential. The effects of the presence of positively charged dust fluid, the external magnetic field, and the obliqueness are obtained. The results of the present investigation may be applicable to some plasma environments, such …
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.