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Ordinary Differential Equations and Applied Dynamics Commons™
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- Stability (2)
- Approximation methods (1)
- Bifurcation analysis (1)
- Caputo derivative (1)
- Carriers (1)
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- Chebyshev polynomials and series (1)
- Cholera (1)
- Collocation points (1)
- Daftardar-Jafari iterative method (1)
- Dichotomic Maps (1)
- Differential transform method (1)
- Generalized Taylor’s formula (1)
- Generalized differential transform method (1)
- Infectious diseases (1)
- MATLAB. (1)
- Mathieu equation (1)
- Mixed linear integro delay differential-difference equations (1)
- Modified Adomian decomposition (1)
- Neutral Type (1)
- Non-linear problems (1)
- Nonlinear PDEs (1)
- Nonlinear delayed model (1)
- Nonlinear differential equation (1)
- Numerical simulation (1)
- Oscillation (1)
- Partial Dynamic Equation (1)
- Singular boundary value problems (1)
- Tapered fin (1)
- Time Scales (1)
- Wave variables (1)
Articles 1 - 8 of 8
Full-Text Articles in Ordinary Differential Equations and Applied Dynamics
On Stability Of Dynamic Equations On Time Scales Via Dichotomic Maps, Veysel F. Hatipoğlu, Zeynep F. Koçak, Deniz Uçar
On Stability Of Dynamic Equations On Time Scales Via Dichotomic Maps, Veysel F. Hatipoğlu, Zeynep F. Koçak, Deniz Uçar
Applications and Applied Mathematics: An International Journal (AAM)
Dichotomic maps are used to check the stability of ordinary differential equations and difference equations. In this paper, this method is extended to dynamic equations on time scales; the stability and asymptotic stability to the trivial solution of the first order system of dynamic equations are examined using dichotomic and strictly dichotomic maps. This method, in dynamic equations, also involves Lyapunov’s direct method.
On The Numerical Solution Of Linear Fredholm-Volterra İntegro Differential Difference Equations With Piecewise İntervals, Mustafa Gülsu, Yalçın Öztürk
On The Numerical Solution Of Linear Fredholm-Volterra İntegro Differential Difference Equations With Piecewise İntervals, Mustafa Gülsu, Yalçın Öztürk
Applications and Applied Mathematics: An International Journal (AAM)
The numerical solution of a mixed linear integro delay differential-difference equation with piecewise interval is presented using the Chebyshev collocation method. The aim of this article is to present an efficient numerical procedure for solving a mixed linear integro delay differential difference equations. Our method depends mainly on a Chebyshev expansion approach. This method transforms a mixed linear integro delay differential-difference equations and the given conditions into a matrix equation which corresponds to a system of linear algebraic equation. The reliability and efficiency of the proposed scheme are demonstrated by some numerical experiments and performed on the computer algebraic system …
Investigation Of Nonlinear Problems Of Heat Conduction In Tapered Cooling Fins Via Symbolic Programming, Hooman Fatoorehchi, Hossein Abolghasemi
Investigation Of Nonlinear Problems Of Heat Conduction In Tapered Cooling Fins Via Symbolic Programming, Hooman Fatoorehchi, Hossein Abolghasemi
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, symbolic programming is employed to handle a mathematical model representing conduction in heat dissipating fins with triangular profiles. As the first part of the analysis, the Modified Adomian Decomposition Method (MADM) is converted into a piece of computer code in MATLAB to seek solution for the mentioned problem with constant thermal conductivity (a linear problem). The results show that the proposed solution converges to the analytical solution rapidly. Afterwards, the code is extended to calculate Adomian polynomials and implemented to the similar, but more generalized, problem involving a power law dependence of thermal conductivity on temperature. The …
Applying Differential Transform Method To Nonlinear Partial Differential Equations: A Modified Approach, Marwan T. Alquran
Applying Differential Transform Method To Nonlinear Partial Differential Equations: A Modified Approach, Marwan T. Alquran
Applications and Applied Mathematics: An International Journal (AAM)
This paper proposes another use of the Differential transform method (DTM) in obtaining approximate solutions to nonlinear partial differential equations (PDEs). The idea here is that a PDE can be converted to an ordinary differential equation (ODE) upon using a wave variable, then applying the DTM to the resulting ODE. Three equations, namely, Benjamin-Bona-Mahony (BBM), Cahn-Hilliard equation and Gardner equation are considered in this study. The proposed method reduces the size of the numerical computations and use less rules than the usual DTM method used for multi-dimensional PDEs. The results show that this new approach gives very accurate solutions.
Solving Singular Boundary Value Problems Using Daftardar-Jafari Method, H. Jafari, M. Ahmadi, S. Sadeghi
Solving Singular Boundary Value Problems Using Daftardar-Jafari Method, H. Jafari, M. Ahmadi, S. Sadeghi
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we apply the suggested iterative method by Daftardar and Jafari hereafter called Daftardar-Jafari method for solving singular boundary value problems. In the implementation of this new method, one does not need the computation of the derivative of the so-called Adomian polynomials. The method is quite efficient and is practically well suited for use in these problems. Two illustrative examples has been presented.
Modeling And Analysis Of The Spread Of An Infectious Disease Cholera With Environmental Fluctuations, Manju Agarwal, Vinay Verma
Modeling And Analysis Of The Spread Of An Infectious Disease Cholera With Environmental Fluctuations, Manju Agarwal, Vinay Verma
Applications and Applied Mathematics: An International Journal (AAM)
A nonlinear delayed mathematical model with immigration for the spread of an infectious disease cholera with carriers in the environment is proposed and analyzed. It is assumed that all susceptible are affected by carrier population density. The carrier population density is assumed to follow the logistic model and grows due to conducive human population density related factors. The model is analyzed by stability theory of differential equations and computer simulation. Both the disease-free (DFE), (CFE) and endemic equilibria are found and their stability investigated. Bifurcation analyses about endemic equilibrium are also carried out analytically using the theory of differential equations. …
Oscillation Of Neutral Partial Dynamic Equations, Deniz Uçar, Yaşar Bolat
Oscillation Of Neutral Partial Dynamic Equations, Deniz Uçar, Yaşar Bolat
Applications and Applied Mathematics: An International Journal (AAM)
This paper is concerned with the oscillation of solutions of a certain more general neutral type dynamic equation. We establish within the necessary and sufficient conditions for the oscillation of its solutions.
An Approximate Solution Of The Mathieu Fractional Equation By Using The Generalized Differential Transform Method (Gdtm), H. S. Najafi, S. R. Mirshafaei, E. A. Toroqi
An Approximate Solution Of The Mathieu Fractional Equation By Using The Generalized Differential Transform Method (Gdtm), H. S. Najafi, S. R. Mirshafaei, E. A. Toroqi
Applications and Applied Mathematics: An International Journal (AAM)
The generalized differential transform method (GDTM) is a powerful tool for solving fractional equations. In this paper we solve the Mathieu fractional equation by this method. The approximate solutions obtained are compared with the exact solution. We also show that if both differential orders decrease, we can still have an approximate solution in the different interval of p.