Numerical Solution Of Pde S Using The Method Of Lines
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Numerical Solution Of Pde S Using The Method Of Lines
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Author : R. L. May
language : en
Publisher:
Release Date : 1990
Numerical Solution Of Pde S Using The Method Of Lines written by R. L. May and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Differential equations, Partial categories.
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.
Method Of Lines Pde Analysis In Biomedical Science And Engineering
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Author : William E. Schiesser
language : en
Publisher: John Wiley & Sons
Release Date : 2016-04-18
Method Of Lines Pde Analysis In Biomedical Science And Engineering written by William E. Schiesser and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-18 with Mathematics categories.
Presents the methodology and applications of ODE and PDE models within biomedical science and engineering With an emphasis on the method of lines (MOL) for partial differential equation (PDE) numerical integration, Method of Lines PDE Analysis in Biomedical Science and Engineering demonstrates the use of numerical methods for the computer solution of PDEs as applied to biomedical science and engineering (BMSE). Written by a well-known researcher in the field, the book provides an introduction to basic numerical methods for initial/boundary value PDEs before moving on to specific BMSE applications of PDEs. Featuring a straightforward approach, the book’s chapters follow a consistent and comprehensive format. First, each chapter begins by presenting the model as an ordinary differential equation (ODE)/PDE system, including the initial and boundary conditions. Next, the programming of the model equations is introduced through a series of R routines that primarily implement MOL for PDEs. Subsequently, the resulting numerical and graphical solution is discussed and interpreted with respect to the model equations. Finally, each chapter concludes with a review of the numerical algorithm performance, general observations and results, and possible extensions of the model. Method of Lines PDE Analysis in Biomedical Science and Engineering also includes: Examples of MOL analysis of PDEs, including BMSE applications in wave front resolution in chromatography, VEGF angiogenesis, thermographic tumor location, blood-tissue transport, two fluid and membrane mass transfer, artificial liver support system, cross diffusion epidemiology, oncolytic virotherapy, tumor cell density in glioblastomas, and variable grids Discussions on the use of R software, which facilitates immediate solutions to differential equation problems without having to first learn the basic concepts of numerical analysis for PDEs and the programming of PDE algorithms A companion website that provides source code for the R routines Method of Lines PDE Analysis in Biomedical Science and Engineering is an introductory reference for researchers, scientists, clinicians, medical researchers, mathematicians, statisticians, chemical engineers, epidemiologists, and pharmacokineticists as well as anyone interested in clinical applications and the interpretation of experimental data with differential equation models. The book is also an ideal textbook for graduate-level courses in applied mathematics, BMSE, biology, biophysics, biochemistry, medicine, and engineering.
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."
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
A Compendium Of Partial Differential Equation Models
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Author : William E. Schiesser
language : en
Publisher: Cambridge University Press
Release Date : 2009-03-16
A Compendium Of Partial Differential Equation Models written by William E. Schiesser and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-03-16 with Computers categories.
Presents numerical methods and computer code in Matlab for the solution of ODEs and PDEs with detailed line-by-line discussion.
Numerical Solution Of Time Dependent Advection Diffusion Reaction Equations
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Author : Willem Hundsdorfer
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Numerical Solution Of Time Dependent Advection Diffusion Reaction Equations written by Willem Hundsdorfer and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Technology & Engineering categories.
Unique book on Reaction-Advection-Diffusion problems
Method Of Lines Solution Of The Korteweg De Vries Equation
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Author :
language : en
Publisher:
Release Date : 1993
Method Of Lines Solution Of The Korteweg De Vries Equation written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with categories.
The Korteweg-de Vries equation (KdVE) is a classical nonlinear partial differential equation (PDE) originally formulated to model shallow water flow. In addition to the applications in hydrodynamics, the KdVE has been studied to elucidate interesting mathematical properties. In particular, the KDVE balances front sharpening and dispersion to produce solitons, i.e., traveling waves that do not change shape or speed. In this paper, we compute a solution of the KdVE by the method of lines (MOL) and compare this numerical solution with the analytical solution of the KdVE. In a second numerical solution, we demonstrate how solitons of the KdVE traveling at different velocities can merge and emerge. The numerical procedure described in the paper demonstrates the ease with which the MOL can be applied to the solution of PDEs using established numerical approximations implemented in library routines.
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.
Spline Collocation Methods For Partial Differential Equations
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Author : William E. Schiesser
language : en
Publisher: John Wiley & Sons
Release Date : 2017-05-08
Spline Collocation Methods For Partial Differential Equations written by William E. Schiesser and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-05-08 with Mathematics categories.
A comprehensive approach to numerical partial differential equations Spline Collocation Methods for Partial Differential Equations combines the collocation analysis of partial differential equations (PDEs) with the method of lines (MOL) in order to simplify the solution process. Using a series of example applications, the author delineates the main features of the approach in detail, including an established mathematical framework. The book also clearly demonstrates that spline collocation can offer a comprehensive method for numerical integration of PDEs when it is used with the MOL in which spatial (boundary value) derivatives are approximated with splines, including the boundary conditions. R, an open-source scientific programming system, is used throughout for programming the PDEs and numerical algorithms, and each section of code is clearly explained. As a result, readers gain a complete picture of the model and its computer implementation without having to fill in the details of the numerical analysis, algorithms, or programming. The presentation is not heavily mathematical, and in place of theorems and proofs, detailed example applications are provided. Appropriate for scientists, engineers, and applied mathematicians, Spline Collocation Methods for Partial Differential Equations: Introduces numerical methods by first presenting basic examples followed by more complicated applications Employs R to illustrate accurate and efficient solutions of the PDE models Presents spline collocation as a comprehensive approach to the numerical integration of PDEs and an effective alternative to other, well established methods Discusses how to reproduce and extend the presented numerical solutions Identifies the use of selected algorithms, such as the solution of nonlinear equations and banded or sparse matrix processing Features a companion website that provides the related R routines Spline Collocation Methods for Partial Differential Equations is a valuable reference and/or self-study guide for academics, researchers, and practitioners in applied mathematics and engineering, as well as for advanced undergraduates and graduate-level students.
