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Numerical Solution of Partial Differential Equations

Numerical Solution of Partial Differential Equations Author K. W. Morton
ISBN-10 9781139443203
Release 2005-04-11
Pages
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This is the 2005 second edition of a highly successful and well-respected textbook on the numerical techniques used to solve partial differential equations arising from mathematical models in science, engineering and other fields. The authors maintain an emphasis on finite difference methods for simple but representative examples of parabolic, hyperbolic and elliptic equations from the first edition. However this is augmented by new sections on finite volume methods, modified equation analysis, symplectic integration schemes, convection-diffusion problems, multigrid, and conjugate gradient methods; and several sections, including that on the energy method of analysis, have been extensively rewritten to reflect modern developments. Already an excellent choice for students and teachers in mathematics, engineering and computer science departments, the revised text includes more latest theoretical and industrial developments.



Numerical Solution of Partial Differential Equations by the Finite Element Method

Numerical Solution of Partial Differential Equations by the Finite Element Method Author Claes Johnson
ISBN-10 9780486131597
Release 2012-05-23
Pages 288
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An accessible introduction to the finite element method for solving numeric problems, this volume offers the keys to an important technique in computational mathematics. Suitable for advanced undergraduate and graduate courses, it outlines clear connections with applications and considers numerous examples from a variety of science- and engineering-related specialties.This text encompasses all varieties of the basic linear partial differential equations, including elliptic, parabolic and hyperbolic problems, as well as stationary and time-dependent problems. Additional topics include finite element methods for integral equations, an introduction to nonlinear problems, and considerations of unique developments of finite element techniques related to parabolic problems, including methods for automatic time step control. The relevant mathematics are expressed in non-technical terms whenever possible, in the interests of keeping the treatment accessible to a majority of students.



Numerical Solution of Partial Differential Equations

Numerical Solution of Partial Differential Equations Author Gordon D. Smith
ISBN-10 0198596502
Release 1985
Pages 337
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Substantially revised, this authoritative study covers the standard finite difference methods of parabolic, hyperbolic, and elliptic equations, and includes the concomitant theoretical work on consistency, stability, and convergence. The new edition includes revised and greatly expanded sections on stability based on the Lax-Richtmeyer definition, the application of Pade approximants to systems of ordinary differential equations for parabolic and hyperbolic equations, and a considerably improved presentation of iterative methods. A fast-paced introduction to numerical methods, this will be a useful volume for students of mathematics and engineering, and for postgraduates and professionals who need a clear, concise grounding in this discipline.



The Numerical Solution of Ordinary and Partial Differential Equations

The Numerical Solution of Ordinary and Partial Differential Equations Author Granville Sewell
ISBN-10 9789814635110
Release 2014-12-16
Pages 348
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This book presents methods for the computational solution of differential equations, both ordinary and partial, time-dependent and steady-state. Finite difference methods are introduced and analyzed in the first four chapters, and finite element methods are studied in chapter five. A very general-purpose and widely-used finite element program, PDE2D, which implements many of the methods studied in the earlier chapters, is presented and documented in Appendix A. The book contains the relevant theory and error analysis for most of the methods studied, but also emphasizes the practical aspects involved in implementing the methods. Students using this book will actually see and write programs (FORTRAN or MATLAB) for solving ordinary and partial differential equations, using both finite differences and finite elements. In addition, they will be able to solve very difficult partial differential equations using the software PDE2D, presented in Appendix A. PDE2D solves very general steady-state, time-dependent and eigenvalue PDE systems, in 1D intervals, general 2D regions, and a wide range of simple 3D regions. Contents:Direct Solution of Linear SystemsInitial Value Ordinary Differential EquationsThe Initial Value Diffusion ProblemThe Initial Value Transport and Wave ProblemsBoundary Value ProblemsThe Finite Element MethodsAppendix A — Solving PDEs with PDE2DAppendix B — The Fourier Stability MethodAppendix C — MATLAB ProgramsAppendix D — Answers to Selected Exercises Readership: Undergraduate, graduate students and researchers. Key Features:The discussion of stability, absolute stability and stiffness in Chapter 1 is clearer than in other textsStudents will actually learn to write programs solving a range of simple PDEs using the finite element method in chapter 5In Appendix A, students will be able to solve quite difficult PDEs, using the author's software package, PDE2D. (a free version is available which solves small to moderate sized problems)Keywords:Differential Equations;Partial Differential Equations;Finite Element Method;Finite Difference Method;Computational Science;Numerical AnalysisReviews: "This book is very well written and it is relatively easy to read. The presentation is clear and straightforward but quite rigorous. This book is suitable for a course on the numerical solution of ODEs and PDEs problems, designed for senior level undergraduate or beginning level graduate students. The numerical techniques for solving problems presented in the book may also be useful for experienced researchers and practitioners both from universities or industry." Andrzej Icha Pomeranian Academy in Słupsk Poland



Numerical Solution of Partial Differential Equations in Science and Engineering

Numerical Solution of Partial Differential Equations in Science and Engineering Author Leon Lapidus
ISBN-10 9781118031216
Release 2011-02-14
Pages 677
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From the reviews of Numerical Solution of Partial Differential Equations in Science and Engineering: "The book by Lapidus and Pinder is a very comprehensive, even exhaustive, survey of the subject . . . [It] is unique in that it covers equally finite difference and finite element methods." Burrelle's "The authors have selected an elementary (but not simplistic) mode of presentation. Many different computational schemes are described in great detail . . . Numerous practical examples and applications are described from beginning to the end, often with calculated results given." Mathematics of Computing "This volume . . . devotes its considerable number of pages to lucid developments of the methods [for solving partial differential equations] . . . the writing is very polished and I found it a pleasure to read!" Mathematics of Computation Of related interest . . . NUMERICAL ANALYSIS FOR APPLIED SCIENCE Myron B. Allen and Eli L. Isaacson. A modern, practical look at numerical analysis, this book guides readers through a broad selection of numerical methods, implementation, and basic theoretical results, with an emphasis on methods used in scientific computation involving differential equations. 1997 (0-471-55266-6) 512 pp. APPLIED MATHEMATICS Second Edition, J. David Logan. Presenting an easily accessible treatment of mathematical methods for scientists and engineers, this acclaimed work covers fluid mechanics and calculus of variations as well as more modern methods-dimensional analysis and scaling, nonlinear wave propagation, bifurcation, and singular perturbation. 1996 (0-471-16513-1) 496 pp.



Numerical Solutions of Partial Differential Equations

Numerical Solutions of Partial Differential Equations Author Silvia Bertoluzza
ISBN-10 9783764389406
Release 2009-03-13
Pages 202
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This book presents some of the latest developments in numerical analysis and scientific computing. Specifically, it covers central schemes, error estimates for discontinuous Galerkin methods, and the use of wavelets in scientific computing.



Numerical Solutions for Partial Differential Equations

Numerical Solutions for Partial Differential Equations Author Victor Grigor'e Ganzha
ISBN-10 9781351427500
Release 2017-11-22
Pages 347
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Partial differential equations (PDEs) play an important role in the natural sciences and technology, because they describe the way systems (natural and other) behave. The inherent suitability of PDEs to characterizing the nature, motion, and evolution of systems, has led to their wide-ranging use in numerical models that are developed in order to analyze systems that are not otherwise easily studied. Numerical Solutions for Partial Differential Equations contains all the details necessary for the reader to understand the principles and applications of advanced numerical methods for solving PDEs. In addition, it shows how the modern computer system algebra Mathematica® can be used for the analytic investigation of such numerical properties as stability, approximation, and dispersion.



Numerical Solution of Partial Differential Equations on Parallel Computers

Numerical Solution of Partial Differential Equations on Parallel Computers Author Are Magnus Bruaset
ISBN-10 9783540316190
Release 2006-03-05
Pages 482
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Since the dawn of computing, the quest for a better understanding of Nature has been a driving force for technological development. Groundbreaking achievements by great scientists have paved the way from the abacus to the supercomputing power of today. When trying to replicate Nature in the computer’s silicon test tube, there is need for precise and computable process descriptions. The scienti?c ?elds of Ma- ematics and Physics provide a powerful vehicle for such descriptions in terms of Partial Differential Equations (PDEs). Formulated as such equations, physical laws can become subject to computational and analytical studies. In the computational setting, the equations can be discreti ed for ef?cient solution on a computer, leading to valuable tools for simulation of natural and man-made processes. Numerical so- tion of PDE-based mathematical models has been an important research topic over centuries, and will remain so for centuries to come. In the context of computer-based simulations, the quality of the computed results is directly connected to the model’s complexity and the number of data points used for the computations. Therefore, computational scientists tend to ?ll even the largest and most powerful computers they can get access to, either by increasing the si e of the data sets, or by introducing new model terms that make the simulations more realistic, or a combination of both. Today, many important simulation problems can not be solved by one single computer, but calls for parallel computing.



Asymptotic Analysis and the Numerical Solution of Partial Differential Equations

Asymptotic Analysis and the Numerical Solution of Partial Differential Equations Author Hans G. Kaper
ISBN-10 0585319677
Release 1991-02-25
Pages 286
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Integrates two fields generally held to be incompatible, if not downright antithetical, in 16 lectures from a February 1990 workshop at the Argonne National Laboratory, Illinois. The topics, of interest to industrial and applied mathematicians, analysts, and computer scientists, include singular per



Partial Differential Equations

Partial Differential Equations Author J. Necas
ISBN-10 1584880228
Release 1999-07-23
Pages 360
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As a satellite conference of the 1998 International Mathematical Congress and part of the celebration of the 650th anniversary of Charles University, the Partial Differential Equations Theory and Numerical Solution conference was held in Prague in August, 1998. With its rich scientific program, the conference provided an opportunity for almost 200 participants to gather and discuss emerging directions and recent developments in partial differential equations (PDEs). This volume comprises the Proceedings of that conference. In it, leading specialists in partial differential equations, calculus of variations, and numerical analysis present up-to-date results, applications, and advances in numerical methods in their fields. Conference organizers chose the contributors to bring together the scientists best able to present a complex view of problems, starting from the modeling, passing through the mathematical treatment, and ending with numerical realization. The applications discussed include fluid dynamics, semiconductor technology, image analysis, motion analysis, and optimal control. The importance and quantity of research carried out around the world in this field makes it imperative for researchers, applied mathematicians, physicists and engineers to keep up with the latest developments. With its panel of international contributors and survey of the recent ramifications of theory, applications, and numerical methods, Partial Differential Equations: Theory and Numerical Solution provides a convenient means to that end.



Numerical Solution of Partial Differential Equations

Numerical Solution of Partial Differential Equations Author T. Meis
ISBN-10 9781461258858
Release 2012-12-06
Pages 556
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This book is the result of two courses of lectures given at the University of Cologne in Germany in 1974/75. The majority of the students were not familiar with partial differential equations and functional analysis. This explains why Sections 1, 2, 4 and 12 contain some basic material and results from these areas. The three parts of the book are largely independent of each other and can be read separately. Their topics are: initial value problems, boundary value problems, solutions of systems of equations. There is much emphasis on theoretical considerations and they are discussed as thoroughly as the algorithms which are presented in full detail and together with the programs. We believe that theoretical and practical applications are equally important for a genuine understa- ing of numerical mathematics. When writing this book, we had considerable help and many discussions with H. W. Branca, R. Esser, W. Hackbusch and H. Multhei. H. Lehmann, B. Muller, H. J. Niemeyer, U. Schulte and B. Thomas helped with the completion of the programs and with several numerical calculations. Springer-Verlag showed a lot of patience and under standing during the course of the production of the book. We would like to use the occasion of this preface to express our thanks to all those who assisted in our sometimes arduous task.



Partial Differential Equations with Numerical Methods

Partial Differential Equations with Numerical Methods Author Stig Larsson
ISBN-10 9783540887058
Release 2008-12-05
Pages 262
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The main theme is the integration of the theory of linear PDE and the theory of finite difference and finite element methods. For each type of PDE, elliptic, parabolic, and hyperbolic, the text contains one chapter on the mathematical theory of the differential equation, followed by one chapter on finite difference methods and one on finite element methods. The chapters on elliptic equations are preceded by a chapter on the two-point boundary value problem for ordinary differential equations. Similarly, the chapters on time-dependent problems are preceded by a chapter on the initial-value problem for ordinary differential equations. There is also one chapter on the elliptic eigenvalue problem and eigenfunction expansion. The presentation does not presume a deep knowledge of mathematical and functional analysis. The required background on linear functional analysis and Sobolev spaces is reviewed in an appendix. The book is suitable for advanced undergraduate and beginning graduate students of applied mathematics and engineering.



Numerical Solution of Partial Differential Equations Theory Algorithms and Their Applications

Numerical Solution of Partial Differential Equations  Theory  Algorithms  and Their Applications Author Oleg P. Iliev
ISBN-10 9781461471721
Release 2013-06-04
Pages 327
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One of the current main challenges in the area of scientific computing​ is the design and implementation of accurate numerical models for complex physical systems which are described by time dependent coupled systems of nonlinear PDEs. This volume integrates the works of experts in computational mathematics and its applications, with a focus on modern algorithms which are at the heart of accurate modeling: adaptive finite element methods, conservative finite difference methods and finite volume methods, and multilevel solution techniques. Fundamental theoretical results are revisited in survey articles and new techniques in numerical analysis are introduced. Applications showcasing the efficiency, reliability and robustness of the algorithms in porous media, structural mechanics and electromagnetism are presented. Researchers and graduate students in numerical analysis and numerical solutions of PDEs and their scientific computing applications will find this book useful.



Group Explicit Methods for the Numerical Solution of Partial Differential Equations

Group Explicit Methods for the Numerical Solution of Partial Differential Equations Author David J. Evans
ISBN-10 9056990195
Release 1997-05-22
Pages 480
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A new class of methods, termed "group explicit methods," is introduced in this text. Their applications to solve parabolic, hyperbolic and elliptic equations are outlined, and the advantages for their implementation on parallel computers clearly portrayed. Also included are the introductory and fundamental concepts from which the new methods are derived, and on which they are dependent. With the increasing advent of parallel computing into all aspects of computational mathematics, there is no doubt that the new methods will be widely used.



Innovative Methods for Numerical Solutions of Partial Differential Equations

Innovative Methods for Numerical Solutions of Partial Differential Equations Author P. L. Roe
ISBN-10 9789810248109
Release 2002
Pages 382
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This book consists of 20 review articles dedicated to Prof. Philip Roe on the occasion of his 60th birthday and in appreciation of his original contributions to computational fluid dynamics. The articles, written by leading researchers in the field, cover many topics, including theory and applications, algorithm developments and modern computational techniques for industry.



Numerical Solution of Partial Differential Equations

Numerical Solution of Partial Differential Equations Author James H. Bramble
ISBN-10 UOM:39076006610773
Release 1975
Pages
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Numerical Solution of Partial Differential Equations has been writing in one form or another for most of life. You can find so many inspiration from Numerical Solution of Partial Differential Equations also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Numerical Solution of Partial Differential Equations book for free.



Numerical Solution of Partial Differential Equations

Numerical Solution of Partial Differential Equations Author J.G. Gram
ISBN-10 9789401026727
Release 2012-12-06
Pages 271
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This book contains the transcripts of the invited lectures presented at the NATO Advanced Study Institute on "Numerical Solution of Partial Differential Equations". The Study Institute was held at the Netherlands-Norwegian Reactor School, Institutt for Atomenergi, Kjeller, Norway, 20th - 24th August 1973. The members of the Scientific Advisory Committee were: A. R. Mitchell, University of Dundee, Scotland I. HoI and, University of Trondheim, Norway T. Havie, UniverSity of Trondheim, Norway The members of the Organizing Committee were: E. Andersen, Institutt for Atomenergi, Kjeller, Norway G. E. Fladmark, Institutt for Atomenergi, Kjeller, Norway J. G. Gram, Institutt for Atomenergi, Kjeller, Norway The aim of the Study Institute was to bring together mathe maticians and engineers working with numerical methods. The papers presented covered both theory and application of methods for solution of partial differential equations. The topics were finite element methods, finite difference methods, and methods for solution of linear and nonlinear systems of equations with application to continuum mechanics and heat transfer. The total number of participants was 68. Their names are given at the end of the book. The publication of these proceed ings could be realized through the kind cooperation of the lec turers. The Advanced Study Institute was financially sponsored by NATO Scientific Affairs Division. The Organizing Committee wishes to express its gratitude for this support. Valuable assistance was given by Mrs. G.