Computational Partial Differential Equations

Author : Hans Petter Langtangen
Publisher : Springer Science & Business Media
Page : 704 pages
File Size : 54,9 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9783662011706

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Computational Partial Differential Equations by Hans Petter Langtangen Pdf

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.

Author : Jichun Li,Yi-Tung Chen
Publisher : CRC Press
Page : 423 pages
File Size : 42,7 Mb
Release : 2019-09-26
Category : Mathematics
ISBN : 9780429556531

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Computational Partial Differential Equations Using MATLAB® by Jichun Li,Yi-Tung Chen Pdf

In this popular text for an Numerical Analysis course, the authors introduce several major methods of solving various partial differential equations (PDEs) including elliptic, parabolic, and hyperbolic equations. It covers traditional techniques including the classic finite difference method, finite element method, and state-of-the-art numercial methods.The text uniquely emphasizes both theoretical numerical analysis and practical implementation of the algorithms in MATLAB. This new edition includes a new chapter, Finite Value Method, the presentation has been tightened, new exercises and applications are included, and the text refers now to the latest release of MATLAB. Key Selling Points: A successful textbook for an undergraduate text on numerical analysis or methods taught in mathematics and computer engineering. This course is taught in every university throughout the world with an engineering department or school. Competitive advantage broader numerical methods (including finite difference, finite element, meshless method, and finite volume method), provides the MATLAB source code for most popular PDEs with detailed explanation about the implementation and theoretical analysis. No other existing textbook in the market offers a good combination of theoretical depth and practical source codes.

Author : Jichun Li,Yi-Tung Chen
Publisher : CRC Press
Page : 376 pages
File Size : 47,8 Mb
Release : 2008-10-20
Category : Mathematics
ISBN : 9781420089059

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Computational Partial Differential Equations Using MATLAB by Jichun Li,Yi-Tung Chen Pdf

This textbook introduces several major numerical methods for solving various partial differential equations (PDEs) in science and engineering, including elliptic, parabolic, and hyperbolic equations. It covers traditional techniques that include the classic finite difference method and the finite element method as well as state-of-the-art numerical

Author : Hans Petter Langtangen,Aslak Tveito
Publisher : Springer Science & Business Media
Page : 676 pages
File Size : 46,6 Mb
Release : 2012-09-22
Category : Mathematics
ISBN : 9783642182372

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Advanced Topics in Computational Partial Differential Equations by Hans Petter Langtangen,Aslak Tveito Pdf

A gentle introduction to advanced topics such as parallel computing, multigrid methods, and special methods for systems of PDEs. The goal of all chapters is to ‘compute’ solutions to problems, hence algorithmic and software issues play a central role. All software examples use the Diffpack programming environment - some experience with Diffpack is required. There are also some chapters covering complete applications, i.e., the way from a model, expressed as systems of PDEs, through to discretization methods, algorithms, software design, verification, and computational examples. Suitable for readers with a background in basic finite element and finite difference methods for partial differential equations.

Author : Aslak Tveito,Ragnar Winther
Publisher : Springer Science & Business Media
Page : 392 pages
File Size : 52,6 Mb
Release : 2008-01-21
Category : Mathematics
ISBN : 9780387227733

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Introduction to Partial Differential Equations by Aslak Tveito,Ragnar Winther Pdf

Combining both the classical theory and numerical techniques for partial differential equations, this thoroughly modern approach shows the significance of computations in PDEs and illustrates the strong interaction between mathematical theory and the development of numerical methods. Great care has been taken throughout the book to seek a sound balance between these techniques. The authors present the material at an easy pace and exercises ranging from the straightforward to the challenging have been included. In addition there are some "projects" suggested, either to refresh the students memory of results needed in this course, or to extend the theories developed in the text. Suitable for undergraduate and graduate students in mathematics and engineering.

Author : David F. Griffiths,John W. Dold,David J. Silvester
Publisher : Springer
Page : 368 pages
File Size : 44,8 Mb
Release : 2015-09-24
Category : Mathematics
ISBN : 9783319225692

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Essential Partial Differential Equations by David F. Griffiths,John W. Dold,David J. Silvester Pdf

This volume provides an introduction to the analytical and numerical aspects of partial differential equations (PDEs). It unifies an analytical and computational approach for these; the qualitative behaviour of solutions being established using classical concepts: maximum principles and energy methods. Notable inclusions are the treatment of irregularly shaped boundaries, polar coordinates and the use of flux-limiters when approximating hyperbolic conservation laws. The numerical analysis of difference schemes is rigorously developed using discrete maximum principles and discrete Fourier analysis. A novel feature is the inclusion of a chapter containing projects, intended for either individual or group study, that cover a range of topics such as parabolic smoothing, travelling waves, isospectral matrices, and the approximation of multidimensional advection–diffusion problems. The underlying theory is illustrated by numerous examples and there are around 300 exercises, designed to promote and test understanding. They are starred according to level of difficulty. Solutions to odd-numbered exercises are available to all readers while even-numbered solutions are available to authorised instructors. Written in an informal yet rigorous style, Essential Partial Differential Equations is designed for mathematics undergraduates in their final or penultimate year of university study, but will be equally useful for students following other scientific and engineering disciplines in which PDEs are of practical importance. The only prerequisite is a familiarity with the basic concepts of calculus and linear algebra.

Author : Kenneth Eriksson
Publisher : Cambridge University Press
Page : 558 pages
File Size : 46,6 Mb
Release : 1996-09-05
Category : Mathematics
ISBN : 0521567386

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Computational Differential Equations by Kenneth Eriksson Pdf

This textbook on computational mathematics is based on a fusion of mathematical analysis, numerical computation and applications.

Author : Alfio Quarteroni,Alberto Valli
Publisher : Springer Science & Business Media
Page : 551 pages
File Size : 51,7 Mb
Release : 2009-02-11
Category : Mathematics
ISBN : 9783540852681

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Numerical Approximation of Partial Differential Equations by Alfio Quarteroni,Alberto Valli Pdf

Everything is more simple than one thinks but at the same time more complex than one can understand Johann Wolfgang von Goethe To reach the point that is unknown to you, you must take the road that is unknown to you St. John of the Cross This is a book on the numerical approximation ofpartial differential equations (PDEs). Its scope is to provide a thorough illustration of numerical methods (especially those stemming from the variational formulation of PDEs), carry out their stability and convergence analysis, derive error bounds, and discuss the algorithmic aspects relative to their implementation. A sound balancing of theoretical analysis, description of algorithms and discussion of applications is our primary concern. Many kinds of problems are addressed: linear and nonlinear, steady and time-dependent, having either smooth or non-smooth solutions. Besides model equations, we consider a number of (initial-) boundary value problems of interest in several fields of applications. Part I is devoted to the description and analysis of general numerical methods for the discretization of partial differential equations. A comprehensive theory of Galerkin methods and its variants (Petrov Galerkin and generalized Galerkin), as wellas ofcollocationmethods, is devel oped for the spatial discretization. This theory is then specified to two numer ical subspace realizations of remarkable interest: the finite element method (conforming, non-conforming, mixed, hybrid) and the spectral method (Leg endre and Chebyshev expansion).

Author : Hans Petter Langtangen,Aslak Tveito
Publisher : Unknown
Page : 658 pages
File Size : 43,9 Mb
Release : 2007
Category : Electronic
ISBN : OCLC:804622999

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Advanced Topics in Computational Partial Differential Equations by Hans Petter Langtangen,Aslak Tveito Pdf

Author : David Betounes
Publisher : Springer Science & Business Media
Page : 544 pages
File Size : 54,8 Mb
Release : 1998-05-15
Category : Mathematics
ISBN : 0387983007

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Partial Differential Equations for Computational Science by David Betounes Pdf

This book will have strong appeal to interdisciplinary audiences, particularly in regard to its treatments of fluid mechanics, heat equations, and continuum mechanics. There is also a heavy focus on vector analysis. Maple examples, exercises, and an appendix is also included.

Author : Roland Glowinski,Pekka Neittaanmäki
Publisher : Springer Science & Business Media
Page : 294 pages
File Size : 51,9 Mb
Release : 2008-06-26
Category : Science
ISBN : 9781402087585

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Partial Differential Equations by Roland Glowinski,Pekka Neittaanmäki Pdf

For more than 250 years partial di?erential equations have been clearly the most important tool available to mankind in order to understand a large variety of phenomena, natural at ?rst and then those originating from - man activity and technological development. Mechanics, physics and their engineering applications were the ?rst to bene?t from the impact of partial di?erential equations on modeling and design, but a little less than a century ago the Schr ̈ odinger equation was the key opening the door to the application of partial di?erential equations to quantum chemistry, for small atomic and molecular systems at ?rst, but then for systems of fast growing complexity. The place of partial di?erential equations in mathematics is a very particular one: initially, the partial di?erential equations modeling natural phenomena were derived by combining calculus with physical reasoning in order to - press conservation laws and principles in partial di?erential equation form, leading to the wave equation, the heat equation, the equations of elasticity, the Euler and Navier–Stokes equations for ?uids, the Maxwell equations of electro-magnetics, etc. It is in order to solve ‘constructively’ the heat equation that Fourier developed the series bearing his name in the early 19th century; Fourier series (and later integrals) have played (and still play) a fundamental roleinbothpureandappliedmathematics,includingmanyareasquiteremote from partial di?erential equations. On the other hand, several areas of mathematics such as di?erential ge- etry have bene?ted from their interactions with partial di?erential equations.

Author : Ed Bueler
Publisher : SIAM
Page : 407 pages
File Size : 40,6 Mb
Release : 2020-10-22
Category : Mathematics
ISBN : 9781611976311

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PETSc for Partial Differential Equations: Numerical Solutions in C and Python by Ed Bueler Pdf

The Portable, Extensible Toolkit for Scientific Computation (PETSc) is an open-source library of advanced data structures and methods for solving linear and nonlinear equations and for managing discretizations. This book uses these modern numerical tools to demonstrate how to solve nonlinear partial differential equations (PDEs) in parallel. It starts from key mathematical concepts, such as Krylov space methods, preconditioning, multigrid, and Newton’s method. In PETSc these components are composed at run time into fast solvers. Discretizations are introduced from the beginning, with an emphasis on finite difference and finite element methodologies. The example C programs of the first 12 chapters, listed on the inside front cover, solve (mostly) elliptic and parabolic PDE problems. Discretization leads to large, sparse, and generally nonlinear systems of algebraic equations. For such problems, mathematical solver concepts are explained and illustrated through the examples, with sufficient context to speed further development. PETSc for Partial Differential Equations addresses both discretizations and fast solvers for PDEs, emphasizing practice more than theory. Well-structured examples lead to run-time choices that result in high solver performance and parallel scalability. The last two chapters build on the reader’s understanding of fast solver concepts when applying the Firedrake Python finite element solver library. This textbook, the first to cover PETSc programming for nonlinear PDEs, provides an on-ramp for graduate students and researchers to a major area of high-performance computing for science and engineering. It is suitable as a supplement for courses in scientific computing or numerical methods for differential equations.

Author : Hans Petter Langtangen,Svein Linge
Publisher : Springer
Page : 522 pages
File Size : 51,7 Mb
Release : 2017-06-21
Category : Computers
ISBN : 9783319554563

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Finite Difference Computing with PDEs by Hans Petter Langtangen,Svein Linge Pdf

This book is open access under a CC BY 4.0 license. This easy-to-read book introduces the basics of solving partial differential equations by means of finite difference methods. Unlike many of the traditional academic works on the topic, this book was written for practitioners. Accordingly, it especially addresses: the construction of finite difference schemes, formulation and implementation of algorithms, verification of implementations, analyses of physical behavior as implied by the numerical solutions, and how to apply the methods and software to solve problems in the fields of physics and biology.

Author : Uri M. Ascher
Publisher : SIAM
Page : 403 pages
File Size : 42,5 Mb
Release : 2008-09-04
Category : Mathematics
ISBN : 9780898716528

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Numerical Methods for Evolutionary Differential Equations by Uri M. Ascher Pdf

Develops, analyses, and applies numerical methods for evolutionary, or time-dependent, differential problems.

Author : Daniel J. Duffy
Publisher : John Wiley & Sons
Page : 551 pages
File Size : 52,6 Mb
Release : 2022-03-21
Category : Business & Economics
ISBN : 9781119719670

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Numerical Methods in Computational Finance by Daniel J. Duffy Pdf

This book is a detailed and step-by-step introduction to the mathematical foundations of ordinary and partial differential equations, their approximation by the finite difference method and applications to computational finance. The book is structured so that it can be read by beginners, novices and expert users. Part A Mathematical Foundation for One-Factor Problems Chapters 1 to 7 introduce the mathematical and numerical analysis concepts that are needed to understand the finite difference method and its application to computational finance. Part B Mathematical Foundation for Two-Factor Problems Chapters 8 to 13 discuss a number of rigorous mathematical techniques relating to elliptic and parabolic partial differential equations in two space variables. In particular, we develop strategies to preprocess and modify a PDE before we approximate it by the finite difference method, thus avoiding ad-hoc and heuristic tricks. Part C The Foundations of the Finite Difference Method (FDM) Chapters 14 to 17 introduce the mathematical background to the finite difference method for initial boundary value problems for parabolic PDEs. It encapsulates all the background information to construct stable and accurate finite difference schemes. Part D Advanced Finite Difference Schemes for Two-Factor Problems Chapters 18 to 22 introduce a number of modern finite difference methods to approximate the solution of two factor partial differential equations. This is the only book we know of that discusses these methods in any detail. Part E Test Cases in Computational Finance Chapters 23 to 26 are concerned with applications based on previous chapters. We discuss finite difference schemes for a wide range of one-factor and two-factor problems. This book is suitable as an entry-level introduction as well as a detailed treatment of modern methods as used by industry quants and MSc/MFE students in finance. The topics have applications to numerical analysis, science and engineering. More on computational finance and the author’s online courses, see www.datasim.nl.