The Numerical Method Of Lines
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The Numerical Method Of Lines
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Author : William E. Schiesser
language : en
Publisher: Elsevier
Release Date : 2012-07-27
The Numerical Method Of Lines written by William E. Schiesser and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-07-27 with Mathematics categories.
This is the first book on the numerical method of lines, a relatively new method for solving partial differential equations. The Numerical Method of Lines is also the first book to accommodate all major classes of partial differential equations. This is essentially an applications book for computer scientists. The author will separately offer a disk of FORTRAN 77 programs with 250 specific applications, ranging from "Shuttle Launch Simulation" to "Temperature Control of a Nuclear Fuel Rod."
A Method Of Lines In The Numerical Solution Of Schr Dinger Equation
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Author : Lawal Sa'adu
language : en
Publisher: LAP Lambert Academic Publishing
Release Date : 2012
A Method Of Lines In The Numerical Solution Of Schr Dinger Equation written by Lawal Sa'adu and has been published by LAP Lambert Academic Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Differential equations, Partial categories.
The Method of Lines (MOL) has been one of the simplest but effective technique for solving partial differential equations (PDEs) in which all but one dimension is discretized. This work describes numerical solution of 1-dimensional Schrodinger equation using the method of lines approach (MOL) where spatial dimensions were discretized using some finite difference approximation leaving the time dimension to be the only independent variable in the resulting system of initial value problems. The effect of changing the discretization size on the accuracy of the solution procedure versus changing the step size in the integration of the resulting differential equation was also studied with the incorporation of Simpson's rule function in MATLAB.
Adaptive Method Of Lines
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Author : A, Vande Wouwer
language : en
Publisher: CRC Press
Release Date : 2001-04-18
Adaptive Method Of Lines written by A, Vande Wouwer and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-04-18 with Mathematics categories.
The general Method of Lines (MOL) procedure provides a flexible format for the solution of all the major classes of partial differential equations (PDEs) and is particularly well suited to evolutionary, nonlinear wave PDEs. Despite its utility, however, there are relatively few texts that explore it at a more advanced level and reflect the method's
The Method Of Lines Solution Of Partial Differential Equations
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Author : James M. Hyman
language : en
Publisher: Forgotten Books
Release Date : 2015-06-24
The Method Of Lines Solution Of Partial Differential Equations written by James M. Hyman and has been published by Forgotten Books this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-06-24 with Mathematics categories.
Excerpt from The Method of Lines Solution of Partial Differential Equations In this paper we give an analysis of effective strategies for the so-called method of lines solution of the initial boundary value problem for partial differential equations of the form where u.= g(x, t, u, u, u, f ) t- Xxx Xf = fx, t, u, u, u) We also describe a user oriented Fortran subroutine package called MOLlD for the numerical solution of equations of this type using the method of lines. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
The Method Of Lines Solution Of Partial Differential Equations
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Author : James M Hyman
language : en
Publisher: Legare Street Press
Release Date : 2022-10-27
The Method Of Lines Solution Of Partial Differential Equations written by James M Hyman and has been published by Legare Street Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-10-27 with categories.
This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Time Discrete Method Of Lines For Options And Bonds The A Pde Approach
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Author : Gunter H Meyer
language : en
Publisher: World Scientific
Release Date : 2014-11-27
Time Discrete Method Of Lines For Options And Bonds The A Pde Approach written by Gunter H Meyer and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-27 with Business & Economics categories.
Few financial mathematical books have discussed mathematically acceptable boundary conditions for the degenerate diffusion equations in finance. In The Time-Discrete Method of Lines for Options and Bonds, Gunter H Meyer examines PDE models for financial derivatives and shows where the Fichera theory requires the pricing equation at degenerate boundary points, and what modifications of it lead to acceptable tangential boundary conditions at non-degenerate points on computational boundaries when no financial data are available.Extensive numerical simulations are carried out with the method of lines to examine the influence of the finite computational domain and of the chosen boundary conditions on option and bond prices in one and two dimensions, reflecting multiple assets, stochastic volatility, jump diffusion and uncertain parameters. Special emphasis is given to early exercise boundaries, prices and their derivatives near expiration. Detailed graphs and tables are included which may serve as benchmark data for solutions found with competing numerical methods.
Method Of Lines Analysis Of Turing Models
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Author : W. E. Schiesser
language : en
Publisher: World Scientific Publishing Company
Release Date : 2017
Method Of Lines Analysis Of Turing Models written by W. E. Schiesser and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with Mathematics categories.
This book is directed toward the numerical integration (solution) of a system of partial differential equations (PDEs) that describes a combination of chemical reaction and diffusion, that is, reaction-diffusion PDEs. The particular form of the PDEs corresponds to a system discussed by Alan Turing and is therefore termed a Turing model. Specifically, Turing considered how a reaction-diffusion system can be formulated that does not have the usual smoothing properties of a diffusion (dispersion) system, and can, in fact, develop a spatial variation that might be interpreted as a form of morphogenesis, so he termed the chemicals as morphogens. Turing alluded to the important impact computers would have in the study of a morphogenic PDE system, but at the time (1952), computers were still not readily available. Therefore, his paper is based on analytical methods. Although computers have since been applied to Turing models, computer-based analysis is still not facilitated by a discussion of numerical algorithms and a readily available system of computer routines. The intent of this book is to provide a basic discussion of numerical methods and associated computer routines for reaction-diffusion systems of varying form. The presentation has a minimum of formal mathematics. Rather, the presentation is in terms of detailed examples, presented at an introductory level. This format should assist readers who are interested in developing computer-based analysis for reaction-diffusion PDE systems without having to first study numerical methods and computer programming (coding). The numerical examples are discussed in terms of: (1) numerical integration of the PDEs to demonstrate the spatiotemporal features of the solutions and (2) a numerical eigenvalue analysis that corroborates the observed temporal variation of the solutions. The resulting temporal variation of the 2D and 3D plots demonstrates how the solutions evolve dynamically, including oscillatory long-term behavior. In all of the examples, routines in R are presented and discussed in detail. The routines are available through this link so that the reader can execute the PDE models to reproduce the reported solutions, then experiment with the models, including extensions and application to alternative models.
Method Of Lines Analysis Of Turing Models
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Author : Schiesser William E
language : en
Publisher: World Scientific
Release Date : 2017-06-28
Method Of Lines Analysis Of Turing Models written by Schiesser William E and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-06-28 with Mathematics categories.
This book is directed toward the numerical integration (solution) of a system of partial differential equations (PDEs) that describes a combination of chemical reaction and diffusion, that is, reaction-diffusion PDEs. The particular form of the PDEs corresponds to a system discussed by Alan Turing and is therefore termed a Turing model. Specifically, Turing considered how a reaction-diffusion system can be formulated that does not have the usual smoothing properties of a diffusion (dispersion) system, and can, in fact, develop a spatial variation that might be interpreted as a form of morphogenesis, so he termed the chemicals as morphogens. Turing alluded to the important impact computers would have in the study of a morphogenic PDE system, but at the time (1952), computers were still not readily available. Therefore, his paper is based on analytical methods. Although computers have since been applied to Turing models, computer-based analysis is still not facilitated by a discussion of numerical algorithms and a readily available system of computer routines. The intent of this book is to provide a basic discussion of numerical methods and associated computer routines for reaction-diffusion systems of varying form. The presentation has a minimum of formal mathematics. Rather, the presentation is in terms of detailed examples, presented at an introductory level. This format should assist readers who are interested in developing computer-based analysis for reaction-diffusion PDE systems without having to first study numerical methods and computer programming (coding). The numerical examples are discussed in terms of: (1) numerical integration of the PDEs to demonstrate the spatiotemporal features of the solutions and (2) a numerical eigenvalue analysis that corroborates the observed temporal variation of the solutions. The resulting temporal variation of the 2D and 3D plots demonstrates how the solutions evolve dynamically, including oscillatory long-term behavior. In all of the examples, routines in R are presented and discussed in detail. The routines are available through a download link so that the reader can execute the PDE models to reproduce the reported solutions, then experiment with the models, including extensions and application to alternative models.
A Compendium Of Partial Differential Equation Models
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Author : William E. Schiesser
language : en
Publisher:
Release Date : 2009
A Compendium Of Partial Differential Equation Models written by William E. Schiesser and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Differential equations, Partial categories.
Presents numerical methods and computer code in Matlab for the solution of ODEs and PDEs with detailed line-by-line discussion.
Numerical Methods For Partial Differential Equations
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Author : William F. Ames
language : en
Publisher: Academic Press
Release Date : 2014-06-28
Numerical Methods For Partial Differential Equations written by William F. Ames and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-28 with Mathematics categories.
This volume is designed as an introduction to the concepts of modern numerical analysis as they apply to partial differential equations. The book contains many practical problems and their solutions, but at the same time, strives to expose the pitfalls--such as overstability, consistency requirements, and the danger of extrapolation to nonlinear problems methods used on linear problems. Numerical Methods for Partial Differential Equations, Third Edition reflects the great accomplishments that have taken place in scientific computation in the fifteen years since the Second Edition was published. This new edition is a drastic revision of the previous one, with new material on boundary elements, spectral methods, the methods of lines, and invariant methods. At the same time, the new edition retains the self-contained nature of the older version, and shares the clarity of its exposition and the integrity of its presentation. Material on finite elements and finite differences have been merged, and now constitute equal partners Additional material has been added on boundary elements, spectral methods, the method of lines, and invariant methods References have been updated, and reflect the additional material Self-contained nature of the Second Edition has been maintained Very suitable for PDE courses