Numerical simulations of traveling wave solutions in a drift paradox inspired diffusive delay population model

2014 ◽  
Vol 96 ◽  
pp. 95-103 ◽  
Author(s):  
Z. Jackiewicz ◽  
H. Liu ◽  
B. Li ◽  
Y. Kuang
Keyword(s):  
Numerical Simulations ◽  
Traveling Wave ◽  
Population Model ◽  
Traveling Wave Solutions ◽  
Drift Paradox ◽  
Wave Solutions

scholarly journals Five semi analytical and numerical simulations for the fractional nonlinear space-time telegraph equation

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Mostafa M. A. Khater ◽  
Choonkil Park ◽  
Jung Rye Lee ◽  
Mohamed S. Mohamed ◽  
Raghda A. M. Attia
Keyword(s):  
Numerical Simulations ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Approximate Solutions ◽  
Telegraph Equation ◽  
Space Time ◽  
Numerical Techniques ◽  
B Spline ◽  
Wave Solutions ◽  
Adomian Decomposition

AbstractThe accuracy of analytical obtained solutions of the fractional nonlinear space–time telegraph equation that has been constructed in (Hamed and Khater in J. Math., 2020) is checked through five recent semi-analytical and numerical techniques. Adomian decomposition (AD), El Kalla (EK), cubic B-spline (CBS), extended cubic B-spline (ECBS), and exponential cubic B-spline (ExCBS) schemes are used to explain the matching between analytical and approximate solutions, which shows the accuracy of constructed traveling wave solutions. In 1880, Oliver Heaviside derived the considered model to describe the cutting-edge or voltage of an electrified transmission. The matching between solutions has been explained by plotting them in some different sketches.

New exact traveling wave solutions of biological population model via the extended rational sinh-cosh method and the modified Khater method

2019 ◽  
Vol 33 (28) ◽  
pp. 1950338 ◽  
Author(s):  
Hadi Rezazadeh ◽  
Alper Korkmaz ◽  
Mostafa M. A. Khater ◽  
Mostafa Eslami ◽  
Dianchen Lu ◽  
...  
Keyword(s):  
Exact Solutions ◽  
Traveling Wave ◽  
Population Model ◽  
Stability Property ◽  
Traveling Wave Solutions ◽  
Algebraic Methods ◽  
New Exact Solutions ◽  
Wave Solutions ◽  
Biological Population ◽  
The Stability

In this paper, the extended rational sinh-cosh method (ERSCM) and modified Khater method are applied to the biological population model to derive new exact solutions. Moreover, the stability property of some obtained solutions is discussed to show the ability of them for using in the model’s applications. Implementation of the direct algebraic methods, the equations derived by substitution of the predicted solution are solved. It is significant to point out that new traveling wave solutions are found. The present methods are easy to employ and sufficient to determine the solutions.

Analysis of a heterogeneous model for riot dynamics: the effect of censorship of information

2015 ◽  
Vol 27 (3) ◽  
pp. 554-582 ◽  
Author(s):  
H. BERESTYKI ◽  
N. RODRIGUEZ
Keyword(s):  
Numerical Simulations ◽  
Traveling Wave ◽  
Heterogeneous Media ◽  
Traveling Wave Solutions ◽  
Global Solutions ◽  
Open Problems ◽  
Heterogeneous Model ◽  
Wave Solutions ◽  
The Cauchy Problem ◽  
Barrier Problem

This paper is concerned with modelling the dynamics of social outbursts of activity, such as protests or riots. In this sequel to our work in Berestycki et al. (Networks and Heterogeneous Media, vol. 10, no. 3, 1–34), written in collaboration with J-P. Nadal, we model the effect of restriction of information and explore its impact on the existence of upheaval waves. The system involves the coupling of an explicit variable representing the intensity of rioting activity and an underlying (implicit) field of social tension. We prove the existence of global solutions to the Cauchy problem in ${\mathbb R}^d$ as well as the existence of traveling wave solutions in certain parameter regimes. We furthermore explore the effects of heterogeneities in the environment with the help of numerical simulations, which lead to pulsating waves in certain cases. We analyse the effects of periodic domains as well as the barrier problem with the help of numerical simulations. The barrier problem refers to the potential blockage of a wavefront due to a spatial heterogeneity in the system which leads to an area of low excitability (referred to as the barrier). We conclude with a variety of open problems.

Traveling wave solutions of the one-dimensional Boussinesq paradigm equation

2013 ◽  
Author(s):  
V. M. Vassilev ◽  
P. A. Djondjorov ◽  
M. Ts. Hadzhilazova ◽  
I. M. Mladenov
Keyword(s):  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
One Dimensional ◽  
Wave Solutions ◽  
The One
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