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Numerical Solution of Partial Differential Equations in Science and Engineering

Author : Leon Lapidus

Publisher : John Wiley & Sons

Page : 677 pages

File Size : 33,88 MB

Release : 2011-02-14

Category : Mathematics

ISBN : 1118031210

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Book Description

From the reviews of Numerical Solution of PartialDifferential Equations in Science and Engineering: "The book by Lapidus and Pinder is a very comprehensive, evenexhaustive, survey of the subject . . . [It] is unique in that itcovers 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 aredescribed in great detail . . . Numerous practical examples andapplications are described from beginning to the end, often withcalculated results given." Mathematics of Computing "This volume . . . devotes its considerable number of pages tolucid developments of the methods [for solving partial differentialequations] . . . the writing is very polished and I found it apleasure to read!" Mathematics of Computation Of related interest . . . NUMERICAL ANALYSIS FOR APPLIED SCIENCE Myron B. Allen andEli L. Isaacson. A modern, practical look at numerical analysis,this book guides readers through a broad selection of numericalmethods, implementation, and basic theoretical results, with anemphasis on methods used in scientific computation involvingdifferential equations. 1997 (0-471-55266-6) 512 pp. APPLIED MATHEMATICS Second Edition, J. David Logan.Presenting an easily accessible treatment of mathematical methodsfor scientists and engineers, this acclaimed work covers fluidmechanics and calculus of variations as well as more modernmethods-dimensional analysis and scaling, nonlinear wavepropagation, bifurcation, and singular perturbation. 1996(0-471-16513-1) 496 pp.



Numerical Methods for Solving Partial Differential Equations

Author : George F. Pinder

Publisher : John Wiley & Sons

Page : 414 pages

File Size : 18,36 MB

Release : 2018-02-05

Category : Technology & Engineering

ISBN : 1119316383

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Book Description

A comprehensive guide to numerical methods for simulating physical-chemical systems This book offers a systematic, highly accessible presentation of numerical methods used to simulate the behavior of physical-chemical systems. Unlike most books on the subject, it focuses on methodology rather than specific applications. Written for students and professionals across an array of scientific and engineering disciplines and with varying levels of experience with applied mathematics, it provides comprehensive descriptions of numerical methods without requiring an advanced mathematical background. Based on its author’s more than forty years of experience teaching numerical methods to engineering students, Numerical Methods for Solving Partial Differential Equations presents the fundamentals of all of the commonly used numerical methods for solving differential equations at a level appropriate for advanced undergraduates and first-year graduate students in science and engineering. Throughout, elementary examples show how numerical methods are used to solve generic versions of equations that arise in many scientific and engineering disciplines. In writing it, the author took pains to ensure that no assumptions were made about the background discipline of the reader. Covers the spectrum of numerical methods that are used to simulate the behavior of physical-chemical systems that occur in science and engineering Written by a professor of engineering with more than forty years of experience teaching numerical methods to engineers Requires only elementary knowledge of differential equations and matrix algebra to master the material Designed to teach students to understand, appreciate and apply the basic mathematics and equations on which Mathcad and similar commercial software packages are based Comprehensive yet accessible to readers with limited mathematical knowledge, Numerical Methods for Solving Partial Differential Equations is an excellent text for advanced undergraduates and first-year graduate students in the sciences and engineering. It is also a valuable working reference for professionals in engineering, physics, chemistry, computer science, and applied mathematics.



Numerical Partial Differential Equations for Environmental Scientists and Engineers

Author : Daniel R. Lynch

Publisher : Springer Science & Business Media

Page : 390 pages

File Size : 21,50 MB

Release : 2006-06-02

Category : Science

ISBN : 0387236201

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Book Description

For readers with some competence in PDE solution properties, this book offers an interdisciplinary approach to problems occurring in natural environmental media: the hydrosphere, atmosphere, cryosphere, lithosphere, biosphere and ionosphere. It presents two major discretization methods: Finite Difference and Finite Element, plus a section on practical approaches to ill-posed problems. The blend of theory, analysis, and implementation practicality supports solving and understanding complicated problems.



Numerical Solution of Partial Differential Equations on Parallel Computers

Author : Are Magnus Bruaset

Publisher : Springer Science & Business Media

Page : 491 pages

File Size : 41,67 MB

Release : 2006-03-05

Category : Mathematics

ISBN : 3540316191

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Book Description

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.



Numerical Solution of Partial Differential Equations by the Finite Element Method

Author : Claes Johnson

Publisher : Courier Corporation

Page : 290 pages

File Size : 42,55 MB

Release : 2012-05-23

Category : Mathematics

ISBN : 0486131599

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Book Description

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.



Domain Decomposition Methods for the Numerical Solution of Partial Differential Equations

Author : Tarek Mathew

Publisher : Springer Science & Business Media

Page : 775 pages

File Size : 10,41 MB

Release : 2008-06-25

Category : Mathematics

ISBN : 354077209X

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Book Description

Domain decomposition methods are divide and conquer computational methods for the parallel solution of partial differential equations of elliptic or parabolic type. The methodology includes iterative algorithms, and techniques for non-matching grid discretizations and heterogeneous approximations. This book serves as a matrix oriented introduction to domain decomposition methodology. A wide range of topics are discussed include hybrid formulations, Schwarz, and many more.



Computational Partial Differential Equations

Author : Hans Petter Langtangen

Publisher : Springer Science & Business Media

Page : 704 pages

File Size : 47,10 MB

Release : 2013-04-17

Category : Mathematics

ISBN : 3662011700

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Book Description

Targeted at students and researchers in computational sciences who need to develop computer codes for solving PDEs, the exposition here is focused on numerics and software related to mathematical models in solid and fluid mechanics. The book teaches finite element methods, and basic finite difference methods from a computational point of view, with the main emphasis on developing flexible computer programs, using the numerical library Diffpack. Diffpack is explained in detail for problems including model equations in applied mathematics, heat transfer, elasticity, and viscous fluid flow. All the program examples, as well as Diffpack for use with this book, are available on the Internet. XXXXXXX NEUER TEXT This book is for researchers who need to develop computer code for solving PDEs. Numerical methods and the application of Diffpack are explained in detail. Diffpack is a modern C++ development environment that is widely used by industrial scientists and engineers working in areas such as oil exploration, groundwater modeling, and materials testing. All the program examples, as well as a test version of Diffpack, are available for free over the Internet.



Solving PDEs in C++

Author : Yair Shapira

Publisher : SIAM

Page : 775 pages

File Size : 21,68 MB

Release : 2012-06-07

Category : Computers

ISBN : 1611972167

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Book Description

In this much-expanded second edition, author Yair Shapira presents new applications and a substantial extension of the original object-oriented framework to make this popular and comprehensive book even easier to understand and use. It not only introduces the C and C++ programming languages, but also shows how to use them in the numerical solution of partial differential equations (PDEs). The book leads readers through the entire solution process, from the original PDE, through the discretization stage, to the numerical solution of the resulting algebraic system. The high level of abstraction available in C++ is particularly useful in the implementation of complex mathematical objects, such as unstructured mesh, sparse matrix, and multigrid hierarchy, often used in numerical modeling. The well-debugged and tested code segments implement the numerical methods efficiently and transparently in a unified object-oriented approach.



Numerical Solution of Partial Differential Equations

Author : K. W. Morton

Publisher : Cambridge University Press

Page : 287 pages

File Size : 46,12 MB

Release : 2005-04-11

Category : Mathematics

ISBN : 1139443208

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Book Description

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.



Partial Differential Equations for Engineers and Scientists

Author : J. N. Sharma

Publisher : Alpha Science International, Limited

Page : 362 pages

File Size : 38,66 MB

Release : 2009

Category : Mathematics

ISBN :

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Book Description

Partial Differential Equations for Engineers and Scientists presents various well known mathematical techniques such as variable of separable method, integral transform techniques and Green's functions method, integral equations and numerical solutions to solve a number of mathematical problems. This comprehensive and compact text book, primarily designed for advanced undergraduate and postgraduate students in mathematics, physics and engineering is enriched with solved examples and supplemented with a variety of exercises at the end of each chapter. The knowledge of advanced calculus, Fourier series and some understanding about ordinary differential equations, finite differences as well as special functions are the prerequisites for the book. Senior undergraduate and postgraduate students offering courses in partial differential equations, researchers, scientists and engineers working in RD organisations would find the book to be most useful.