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The numerical solution of a generalized Burgers–Huxley equation through a conditionally bounded and symmetry-preserving method

J.E. Macías-Díaz, J. Ruiz-Ramírez, J. Villa
2011 Computers and Mathematics with Applications  
In this article, we propose a non-standard, finite-difference scheme to approximate the solutions of a generalized Burgers-Huxley equation from fluid dynamics.  ...  , it is capable of preserving the boundedness and the positivity of the solutions.  ...  of most of the propositions and to more meaningful simulations.  ... 
doi:10.1016/j.camwa.2011.04.022 fatcat:cc7ur6gfizbsvp5gbqrw2gryzu

A New Class of Difference Methods with Intrinsic Parallelism for Burgers–Fisher Equation

Yueyue Pan, Lifei Wu, Xiaozhong Yang
2020 Mathematical Problems in Engineering  
This paper proposes a new class of difference methods with intrinsic parallelism for solving the BurgersFisher equation.  ...  The PASE-I and PASI-E schemes have obvious parallel computing properties, which show that the difference methods with intrinsic parallelism in this paper are feasible to solve the BurgersFisher equation  ...  [22] presented the numerical solution of the generalized Burgers-Fisher equation on the basis of the nonstandard finite-difference (NSFD) scheme. e positivity, consistency, and boundedness of the scheme  ... 
doi:10.1155/2020/9162563 fatcat:kc33jfuucvb43ijdleexaejube

Exact Finite Difference Scheme and Nonstandard Finite Difference Scheme for Burgers and Burgers-Fisher Equations

Lei Zhang, Lisha Wang, Xiaohua Ding
2014 Journal of Applied Mathematics  
A new version of exact finite difference scheme for Burgers equation and Burgers-Fisher equation is proposed using the solitary wave solution.  ...  We present finite difference schemes for Burgers equation and Burgers-Fisher equation.  ...  Acknowledgments The authors thank the reviewers for giving attention to their paper and for the very helpful suggestions.  ... 
doi:10.1155/2014/597926 fatcat:l3a5ioetdfhuxjuxtpkyvlec3m

Hybrid B-Spline Collocation Method for Solving the Generalized Burgers-Fisher and Burgers-Huxley Equations

Imtiaz Wasim, Muhammad Abbas, Muhammad Amin
2018 Mathematical Problems in Engineering  
In this study, we introduce a new numerical technique for solving nonlinear generalized Burgers-Fisher and Burgers-Huxley equations using hybrid B-spline collocation method.  ...  This technique is based on usual finite difference scheme and Crank-Nicolson method which are used to discretize the time derivative and spatial derivatives, respectively.  ...  [31] developed a new kind of exact finite difference scheme for solving Burgers equation and Burgers-Fisher equation using the solitary wave solution.  ... 
doi:10.1155/2018/6143934 fatcat:4wkb3sap2bgjzi24tl7nrv5izi

Optimal solution error covariance in highly nonlinear problems of variational data assimilation

V. Shutyaev, I. Gejadze, G. J. M. Copeland, F.-X. Le Dimet
2012 Nonlinear Processes in Geophysics  
For mildly nonlinear dynamics, the covariance matrix of the optimal solution error can be approximated by the inverse Hessian of the cost function.  ...  Numerical examples are presented for the model governed by the Burgers equation with a nonlinear viscous term.</p>  ...  All the authors thank the editor and the anonymous reviewers for their useful comments and suggestions. Edited by: O. Talagrand Reviewed by: three anonymous referees  ... 
doi:10.5194/npg-19-177-2012 fatcat:nj6elh34znc7fgthh44nmp6ptu

High-order entropy stable finite difference schemes for nonlinear conservation laws: Finite domains

Travis C. Fisher, Mark H. Carpenter
2013 Journal of Computational Physics  
To the authors' knowledge, this proof of entropy consistency for high-order finite difference methods on bounded domains is new.  ...  Finite difference methods approximately satisfy the governing equation at the solution points, x. Difference methods based solely on the solutions points are considered next.  ...  A newly derived entropy stable weighted essentially non-oscillatory finite difference method is used to simulate problems with shocks and a conservative, entropy stable, narrow-stencil finite difference  ... 
doi:10.1016/j.jcp.2013.06.014 fatcat:q6nkn7dwebfw7oarbkrhlzyrgy

Regularized Regression and Density Estimation based on Optimal Transport

M. Burger, M. Franek, C.-B. Schonlieb
2012 Applied Mathematics Research eXpress  
In order to compute solutions of the variational problems, a regularized optimal transport problem needs to be solved, for which we discuss several formulations and provide a detailed analysis.  ...  method with the Wasserstein metric as a data fidelity.  ...  Acknowledgement The work of M.B. has been supported by the German Science Foundation (DFG) through project  ... 
doi:10.1093/amrx/abs007 fatcat:vzd4gkxnebbkzewwcvbqr4zaty

The non-stationary dynamics of fitness distributions: asexual model with epistasis and standing variation [article]

GUILLAUME MARTIN, Lionel Roques
2016 bioRxiv   pre-print
Others follow the dynamics of quantitative traits determining fitness (Fisher′s geometrical model), imposing a complex but fixed form of mutation effects and epistasis, and often ignoring drift.  ...  Beyond this phase transition, in Fisher′s geometrical model, the full trajectory of fitness and trait distributions takes simple form, robust to details of the mutant phenotype distribution.  ...  Acknowledgments: This work was funded by INRA grant 'MEDIA network' and by the French National  ... 
doi:10.1101/079368 fatcat:vnf4vjlgznakpjcgvmorr6yuzq

McKean Feynman-Kac probabilistic representations of non-linear partial differential equations [article]

Lucas Izydorczyk
2019 arXiv   pre-print
This paper presents a partial state of the art about the topic of representation of generalized Fokker-Planck Partial Differential Equations (PDEs) by solutions of McKean Feynman-Kac Equations (MFKEs)  ...  Motivations come from modeling issues but also from numerical approximation issues in computing the solution of a PDE, arising for instance in the context of stochastic control.  ...  Acknowledgments The work was supported by a public grant as part of the Investissement d'avenir project, reference ANR-11-LABX-0056-LMH, LabEx LMH, in a joint call with Gaspard Monge Program for optimization  ... 
arXiv:1912.03146v1 fatcat:42apyafcercbhdwuf3k5kwwo4y

Analysis of a quasi-reversibility method for a terminal value quasi-linear parabolic problem with measurements [article]

Nguyen Huy Tuan, Vo Anh Khoa, Vo Van Au
2018 arXiv   pre-print
Different from recently developed approaches that consist in the conventional spectral methods, we analyze this new approximation in a variational framework, where the finite element method can be applied  ...  To see the whole skeleton of this method, our main results lie in the analysis of a semi-linear case and we discuss some generalizations where this analysis can be adapted.  ...  The authors would like to thank the anonymous referee(s) and the handling editor(s) for fruitful comments through the significant improvement of this paper. V.A.K acknowledges Prof.  ... 
arXiv:1803.04641v2 fatcat:ggrqrfltmfcjffno5yqyj3ycn4

Existence and spectral instability of bounded spatially periodic traveling waves for scalar viscous balance laws [article]

Enrique Alvarez, Ramon G. Plaza
2020 arXiv   pre-print
This paper studies both existence and spectral stability properties of bounded spatially periodic traveling wave solutions to a large class of scalar viscous balance laws in one space dimension with a  ...  The first family consists of small amplitude waves with finite fundamental period which emerge from a Hopf bifurcation around a critical value of the wave speed.  ...  Examples In this section we present some examples of viscous balance laws of the from (1.1) which satisfy the hypotheses of this paper. 6.1. Burgers-Fisher equation. The Burgers-Fisher equation (cf.  ... 
arXiv:2008.10120v1 fatcat:w67skop4i5b2zg7gtmta2zl62q

Two-time-scale population evolution on a singular landscape

Song Xu, Shuyun Jiao, Pengyao Jiang, Ping Ao
2014 Physical Review E  
The constructed landscape provides a global and coherent description for system's evolutionary dynamics, allowing new biological results to be generated.  ...  Our results showed that Kramers' classical escape formula can be extended to the models with non-Gaussian probability distributions, overcoming constraints in previous methods.  ...  Wang, and other members in the lab for their constructive comments. We thank X. A. Wang for the technical support.  ... 
doi:10.1103/physreve.89.012724 pmid:24580274 fatcat:56vsnz6e5nb5tpors7omfq25q4

Discrete monotone method for space-fractional nonlinear reaction–diffusion equations

Salvador Flores, Jorge E. Macías-Díaz, Ahmed S. Hendy
2019 Advances in Difference Equations  
In that case, the monotone iterative method guarantees the preservation of the positivity and the boundedness of the numerical approximations.  ...  The finite-difference scheme is based on the use of fractional-order centered differences, and it is solved using a monotone iterative technique.  ...  Funding The first author would like to acknowledge the financial support of the National Council for Science and Technology of Mexico (CONACYT).  ... 
doi:10.1186/s13662-019-2267-1 fatcat:ehpok6636nfbbohndtzrxihk74

Pushed, pulled and pushmi-pullyu fronts of the Burgers-FKPP equation [article]

Jing An, Christopher Henderson, Lenya Ryzhik
2021 arXiv   pre-print
We prove convergence of the solutions to a traveling wave in a reference frame centered at a position m_β(t) and study the asymptotics of the front location m_β(t).  ...  We consider the long time behavior of the solutions to the Burgers-FKPP equation with advection of a strength β∈ℝ. This equation exhibits a transition from pulled to pushed front behavior at β_c=2.  ...  a solution to the Burgers-FKPP equation to a traveling wave.  ... 
arXiv:2108.07861v1 fatcat:27s5x627wbg3jlwoyioqgt6aem

Spectral instability of small-amplitude periodic waves for hyperbolic non-Fickian diffusion advection models with logistic source [article]

Enrique Álvarez, Ricardo Murillo, Ramón G. Plaza
2021 arXiv   pre-print
These waves have bounded fundamental period and small-amplitude. In addition, it is shown that these waves are spectrally unstable as solutions to the hyperbolic system.  ...  The production or source term is assumed to be of logistic type. This paper studies the existence and spectral stability properties of spatially periodic traveling wave solutions to this system.  ...  In addition, we present numerical approximations of the waves for a particular example, the hyperbolic Burgers-Fisher model.  ... 
arXiv:2110.03734v1 fatcat:bgsg62a5g5ccpooyseeodeu4yi
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