A Deterministic Particle Method for One-Dimensional Reaction-Diffusion Equations PDF Download
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Author: National Aeronautics and Space Administration (NASA)
Publisher: Createspace Independent Publishing Platform
ISBN: 9781724988430
Category :
Languages : en
Pages : 34
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Book Description
We derive a deterministic particle method for the solution of nonlinear reaction-diffusion equations in one spatial dimension. This deterministic method is an analog of a Monte Carlo method for the solution of these problems that has been previously investigated by the author. The deterministic method leads to the consideration of a system of ordinary differential equations for the positions of suitably defined particles. We then consider the time explicit and implicit methods for this system of ordinary differential equations and we study a Picard and Newton iteration for the solution of the implicit system. Next we solve numerically this system and study the discretization error both analytically and numerically. Numerical computation shows that this deterministic method is automatically adaptive to large gradients in the solution. Mascagni, Michael Unspecified Center NASA-CR-199755, NAS 1.26:199755, RIACS-TR-95-23, NIPS-95-06386 NAS2-13721...
Author: National Aeronautics and Space Administration (NASA)
Publisher: Createspace Independent Publishing Platform
ISBN: 9781724988430
Category :
Languages : en
Pages : 34
Get Book Here
Book Description
We derive a deterministic particle method for the solution of nonlinear reaction-diffusion equations in one spatial dimension. This deterministic method is an analog of a Monte Carlo method for the solution of these problems that has been previously investigated by the author. The deterministic method leads to the consideration of a system of ordinary differential equations for the positions of suitably defined particles. We then consider the time explicit and implicit methods for this system of ordinary differential equations and we study a Picard and Newton iteration for the solution of the implicit system. Next we solve numerically this system and study the discretization error both analytically and numerically. Numerical computation shows that this deterministic method is automatically adaptive to large gradients in the solution. Mascagni, Michael Unspecified Center NASA-CR-199755, NAS 1.26:199755, RIACS-TR-95-23, NIPS-95-06386 NAS2-13721...
Author: Michael Mascagni
Publisher:
ISBN:
Category : Numerical analysis
Languages : en
Pages : 24
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Book Description
Abstract: "We derive a deterministic particle method for the solution of nonlinear reaction-diffusion equations in one spatial dimension. This deterministic method is an analog of a Monte Carlo method for the solution of these problems that has been previously investigated by the author. The deterministic method leads to the consideration of a system of ordinary differential equations for the positions of suitably defined particles. We then consider the time explicit and implicit methods for this system of ordinary differential equations and we study a Picard and Newton iteration for the solution of the implicit system. Next we solve numerically this system and study the discretization error both analytically and numerically. Numerical computation shows that this deterministic method is automatically adaptive to large gradients in the solution."
Author: Yann Brenier
Publisher:
ISBN:
Category :
Languages : en
Pages : 45
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Book Description
Author: Radek Erban
Publisher: Cambridge University Press
ISBN: 1108572995
Category : Mathematics
Languages : en
Pages : 322
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Book Description
This practical introduction to stochastic reaction-diffusion modelling is based on courses taught at the University of Oxford. The authors discuss the essence of mathematical methods which appear (under different names) in a number of interdisciplinary scientific fields bridging mathematics and computations with biology and chemistry. The book can be used both for self-study and as a supporting text for advanced undergraduate or beginning graduate-level courses in applied mathematics. New mathematical approaches are explained using simple examples of biological models, which range in size from simulations of small biomolecules to groups of animals. The book starts with stochastic modelling of chemical reactions, introducing stochastic simulation algorithms and mathematical methods for analysis of stochastic models. Different stochastic spatio-temporal models are then studied, including models of diffusion and stochastic reaction-diffusion modelling. The methods covered include molecular dynamics, Brownian dynamics, velocity jump processes and compartment-based (lattice-based) models.
Author: Dongyong Wang
Publisher:
ISBN: 9781321094428
Category :
Languages : en
Pages : 99
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Book Description
Reaction diffusion equations are widely used to model biological phenomena and in some situation, the spatial dimension can be much larger. Numerical efficiently solving high-dimensional reaction-diffusion equations is a huge challenge. To solve the high-dimensional equation, the ``curse of dimensions" has to be dealt with. Also, an efficiently time integration method is needed to solve the afterwords time dependent problem. The sparse grid technique can deal with the problem, and the semi-implicit integration factor method can handles the second one. The combination of two methods will be an efficient method to solve high-dimensional reaction-diffusion equations.
Author:
Publisher:
ISBN:
Category : Government publications
Languages : en
Pages : 1000
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Book Description
Author: Gabriela Caristi
Publisher: CRC Press
ISBN: 1000117197
Category : Mathematics
Languages : en
Pages : 428
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Book Description
"Based on the proceedings of the International Conference on Reaction Diffusion Systems held recently at the University of Trieste, Italy. Presents new research papers and state-of-the-art surveys on the theory of elliptic, parabolic, and hyperbolic problems, and their related applications. Furnishes incisive contribution by over 40 mathematicians representing renowned institutions in North and South America, Europe, and the Middle East."
Author: Masaharu Taniguchi
Publisher:
ISBN: 9784864970976
Category : Mathematics
Languages : en
Pages : 0
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Book Description
The study on traveling fronts in reaction-diffusion equations is the first step to understand various kinds of propagation phenomena in reaction-diffusion models in natural science. One dimensional traveling fronts have been studied from the 1970s, and multidimensional ones have been studied from around 2005. This volume is a text book for graduate students to start their studies on traveling fronts. Using the phase plane analysis, we study the existence of traveling fronts in several kinds of reaction-diffusion equations. For a nonlinear reaction term, a bistable one is a typical one. For a bistable reaction-diffusion equation, we study the existence and stability of two-dimensional V-form fronts, and we also study pyramidal traveling fronts in three or higher space dimensions. The cross section of a pyramidal traveling front forms a convex polygon. It is known that the limit of a pyramidal traveling front gives a new multidimensional traveling front. For the study the multidimensional traveling front, studying properties of pyramidal traveling fronts plays an important role. In this volume, we study the existence, uniqueness and stability of a pyramidal traveling front as clearly as possible for further studies by graduate students. For a help of their studies, we briefly explain and prove the well-posedness of reaction-diffusion equations and the Schauder estimates and the maximum principles of solutions.Published by Mathematical Society of Japan and distributed by World Scientific Publishing Co. for all markets
Author: Richard Durrett
Publisher:
ISBN:
Category :
Languages : en
Pages : 94
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Book Description
Author: Ludwig Arnold
Publisher: Springer
ISBN: 3540494154
Category : Mathematics
Languages : en
Pages : 336
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Book Description
This volume contains the lecture notes written by the four principal speakers at the C.I.M.E. session on Dynamical Systems held at Montecatini, Italy in June 1994. The goal of the session was to illustrate how methods of dynamical systems can be applied to the study of ordinary and partial differential equations. Topics in random differential equations, singular perturbations, the Conley index theory, and non-linear PDEs were discussed. Readers interested in asymptotic behavior of solutions of ODEs and PDEs and familiar with basic notions of dynamical systems will wish to consult this text.
