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Page 265 of Mathematical Reviews Vol. , Issue 2001A [page]

2001 Mathematical Reviews  
in two spatial dimensions.  ...  Furthermore, these solutions converge to the traveling wave solution of Fisher’s equation. No computational results are presented in the paper. Edward J.  ... 

Analytic Travelling Wave Solutions and Numerical Analysis of Fisher's Equation via Explicit-Implicit FDM

Asif Ahmed, Md. Kamrujjaman
2019 Asian Journal of Advanced Research and Reports  
The analyses focus on to describe the analytic solution in the spatial pattern of travelling wave solutions; especially the solutions are characterized in invariant with respect to translation in space  ...  We study the nonlinear parabolic Fisher's equations for travelling wave solutions.  ...  Tyson and Brazhnik discussed about travelling wave solution for this type of nonlinear equation in two spatial dimensions [6] .  ... 
doi:10.9734/ajarr/2019/v3i330089 fatcat:mpyofjepf5g2pcoqm5blt55xei

Numerical study of Fisher's equation by wavelet Galerkin method

R. C. Mittal, Sumit Kumar
2006 International Journal of Computer Mathematics  
In this work, differential quadrature method is discussed and applied on four examples of representing different types of Fisher's equations.  ...  In this paper, we study the numerical solutions of Fisher's equation and to a nonlinear diffusion equation of the Fisher type by differential quadrature method.  ...  Phys, Vol. pp. 1040-52.[5] Brazhnik, P. and Tyson, J., (1999) 'On traveling wave solutions of Fisher's equation in two spatial dimensions," SIAM J. Appl.  ... 
doi:10.1080/00207160600717758 fatcat:km5ypvdtivbvhnoeqwkumnb3tm

Multiscale modeling and simulation of traveling waves in biology: a review

W. Duncan Martinson, Helen M. Byrne, Philip K. Maini
2019 Rendiconti di Matematica e delle sue Applicazioni. Serie VII  
Fisher's equation is the prototypical example of a problem that admits a traveling wave solution; it is a partial differential equation that was proposed to describe the spread of an advantageous gene.  ...  Traveling waves are a near-ubiquitous phenomenon in mathematical biology, and have been studied in the context of embryonic development, cancer growth, wound healing, and epidemiology.  ...  (both types of models can be formulated in one or more spatial dimensions).  ... 
doaj:0cd7d9f38cf949309735f021dc3c7e10 fatcat:ewhfgwpjxjcc7ehpycrrmlojx4

Page 3851 of Mathematical Reviews Vol. , Issue 94g [page]

1994 Mathematical Reviews  
Summary: “Traveling wave solutions for equations of Fisher’s type are given by a connection from a saddle point to a node, and their velocity for large times is known to be determined by the spatial decay  ...  The author considers the questions of existence and uniqueness for two coupled nonlinear equations, one elliptic and one parabolic, which model the evolution of electric potential and temperature in a  ... 

Waves of extinction from sterile insect release

M.A. Lewis, P. Van Den Driessche
1993 Mathematical Biosciences  
This is the first time traveling wave solutions have been shown for the SIRM.  ...  Employing theoretical models, we show that the sterile insect release method (SIRM) can give rise to traveling waves of fertile insects.  ...  may actively move around, looking for food). (4) The assumption of dispersal in one spatial dimension; a more realistic model would include dispersal in two spatial dimensions rather than one.  ... 
doi:10.1016/0025-5564(93)90067-k pmid:8369600 fatcat:jxlltlmmmzabdgwi6fytt7uqku

Travelling Waves of Attached and Detached Cells in a Wound-Healing Cell Migration Assay

Kerry A. Landman, Anna Q. Cai, Barry D. Hughes
2007 Bulletin of Mathematical Biology  
Approximate travelling wave profiles of the two cell populations are determined asymptotically under certain parameter regimes.  ...  The models yield travelling wave solutions. The minimum wave speed is slower than the minimum Fisher wave speed and its dependence on the cell detachment and reattachment rate parameters is analysed.  ...  In the usual way, we will simplify the two-dimensional spatial geometry of a cell monolayer to only one spatial dimension, by effectively averaging the cell density (cell number per unit area) over the  ... 
doi:10.1007/s11538-007-9206-0 pmid:17577601 fatcat:miftc42vurcujfk6uwiolj5qee

Numerical Solution of Fisher's Equation Using Finite Difference

Sharefa Eisa Ali Alhazmi
2015 Bulletin of Mathematical Sciences and Applications  
The method is based on replacing each terms in the Fisher's equation using finite difference method.  ...  A numerical method is proposed to approximate the numeric solutions of nonlinear Fisher's reaction diffusion equation with finite difference method.  ...  In [14] , some numerical study of Fisher's equation by Adomian's method was proposed. In [15] , the author study a nonlinear reactiondiffusion equation for its traveling waves.  ... 
doi:10.18052/www.scipress.com/bmsa.12.27 fatcat:3tit5uv7wfan3cjkgicdm2ozem

Theoretical analysis and physical interpretation of temporal truncation errors in operator split algorithms

Matthew J. Simpson, Kerry A. Landman
2008 Mathematics and Computers in Simulation  
The analysis allows us to predict the characteristics of the TTE a priori from the structure of the governing equations. The TTE can be interpreted in the form of a pde.  ...  The temporal truncation error (TTE) associated with a noniterative operator split (OS) method for application to a system of m coupled transport partial differential equations (pdes) is analysed.  ...  We also thank Abbey Trewenack for her assistance and two anonymous reviewers for their comments.  ... 
doi:10.1016/j.matcom.2007.01.001 fatcat:7pjirw3a5betvoi63k6yos3pki

Investigation of a Structured Fisher's Equation with Applications in Biochemistry [article]

John T. Nardini, D. M. Bortz
2016 arXiv   pre-print
Fisher's Equation has been used extensively to model experimental wound healing assays due to its simple nature and known traveling wave solutions.  ...  To this end, we derive a structured Fisher's Equation with independent variables of time, space, and biochemical pathway activity level and prove the existence of a self-similar traveling wave solution  ...  As shown in [35, § 11.2] , (1) admits traveling wave solutions of the form u(t, x) = U (z), z = x − ct where c denotes the speed of the traveling wave solution and U (z) denotes the traveling wave profile  ... 
arXiv:1612.05188v1 fatcat:3xq3i3tje5chbjzk7f5sxvh3zy

Traveling Waves of Infection in the Hantavirus Epidemics

G Abramson
2003 Bulletin of Mathematical Biology  
Traveling waves are analyzed in a model of the hantavirus infection in deer mice. The existence of two kinds of wave phenomena is predicted.  ...  An environmental parameter governs a transition between two regimes of propagation. In one of them the front of infection lags behind at a constant rate.  ...  Financial support for the study was partially provided by the Consortium of the Americas for Interdisciplinary Science under a contract from the Los Alamos National Laboratory to the University of New  ... 
doi:10.1016/s0092-8240(03)00013-2 pmid:12749537 fatcat:obaitdenczhgxlwp2lhdg5zrlu

Spatial dynamics in ecology [chapter]

Mark Lewis, Thomas Hillen, Frithjof Lutscher
2009 IAS/Park City Mathematics Series  
Our first step in analyzing population spread is to consider travelling wave solutions of (16).  ...  This also provides a link to two seemingly disjoint areas of analysis in mathematical biology (critical domain size analysis/bifurcation theory for one result and travelling wave/spread rate theory for  ... 
doi:10.1090/pcms/014/03 fatcat:w4y4bydkajdz7m7x3rntgx2ov4

Traveling waves of infection in the Hantavirus epidemics [article]

G. Abramson, V.M. Kenkre, T.L. Yates, R.R. Parmenter
2002 arXiv   pre-print
Traveling waves are analyzed in a model of the Hantavirus infection of deer mice. The existence of two kinds of wave phenomena is predicted.  ...  An environmental parameter governs a transition between two regimes of propagation. In one of them the front of infection lags behind at a constant rate.  ...  Traveling wave solutions of Fisher's equation paradigmatically show how a stable phase invades an unstable one in the form of a front propagating at a certain speed.  ... 
arXiv:physics/0203088v1 fatcat:kcdv7v2dtfeuheomxizuapesry

Numerical Study of Fisher's Equation by Finite Difference Schemes

Bader Saad Alshammari, Daoud Suleiman Mashat
2017 Applied Mathematics  
Moreover, the schemes can be easily applied to a wide class of higher dimension non-linear reaction diffusion equations.  ...  This research paper represents a numerical approximation to three interesting equations of Fisher, which are linear, non-linear and coupled linear one dimensional reaction diffusion equations from population  ...  Acknowledgements Bader Saad Alshammari Conflict of Interest There is no conflict of interest in this research paper.  ... 
doi:10.4236/am.2017.88083 fatcat:tgncksvopbfbjak7de7huma73u

Page 1787 of Mathematical Reviews Vol. , Issue 94c [page]

1994 Mathematical Reviews  
In two dimensions, spontaneous spiral breakup leading to a spatially disorganized electrical wave activity is shown to occur as a direct consequence of this instability.” 94c:92011 92C30 35K57 35Q80 Moll  ...  This paper deals with the long-term behavior of the solutions to such equations in two important classes of algebras.  ... 
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