Computational Partial Differential Equations Using Matlab

Author : Jichun Li,Yi-Tung Chen
Publisher : CRC Press
Page : 423 pages
File Size : 52,6 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 : 51,5 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 : Matthew P. Coleman,Vladislav Bukshtynov
Publisher : Unknown
Page : 0 pages
File Size : 43,6 Mb
Release : 2024-07
Category : Mathematics
ISBN : 1032650869

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An Introduction to Partial Differential Equations with MATLAB by Matthew P. Coleman,Vladislav Bukshtynov Pdf

Author : Jeffery M. Cooper
Publisher : Springer Science & Business Media
Page : 549 pages
File Size : 52,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461217541

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Introduction to Partial Differential Equations with MATLAB by Jeffery M. Cooper Pdf

Overview The subject of partial differential equations has an unchanging core of material but is constantly expanding and evolving. The core consists of solution methods, mainly separation of variables, for boundary value problems with constant coeffi cients in geometrically simple domains. Too often an introductory course focuses exclusively on these core problems and techniques and leaves the student with the impression that there is no more to the subject. Questions of existence, uniqueness, and well-posedness are ignored. In particular there is a lack of connection between the analytical side of the subject and the numerical side. Furthermore nonlinear problems are omitted because they are too hard to deal with analytically. Now, however, the availability of convenient, powerful computational software has made it possible to enlarge the scope of the introductory course. My goal in this text is to give the student a broader picture of the subject. In addition to the basic core subjects, I have included material on nonlinear problems and brief discussions of numerical methods. I feel that it is important for the student to see nonlinear problems and numerical methods at the beginning of the course, and not at the end when we run usually run out of time. Furthermore, numerical methods should be introduced for each equation as it is studied, not lumped together in a final chapter.

Author : Hans Petter Langtangen
Publisher : Springer Science & Business Media
Page : 704 pages
File Size : 47,6 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
Publisher : Chapman & Hall
Page : 128 pages
File Size : 45,5 Mb
Release : 2008-09-26
Category : Electronic
ISBN : 1420099841

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Computational Partial Differential Equations Using MATLAB - Solutions Manual by Jichun Li Pdf

Author : Martin J. Gander,Felix Kwok
Publisher : SIAM
Page : 163 pages
File Size : 52,9 Mb
Release : 2018-01-01
Category : Science
ISBN : 9781611975307

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Numerical Analysis of Partial Differential Equations Using Maple and MATLAB by Martin J. Gander,Felix Kwok Pdf

This book provides an elementary yet comprehensive introduction to the numerical solution of partial differential equations (PDEs). Used to model important phenomena, such as the heating of apartments and the behavior of electromagnetic waves, these equations have applications in engineering and the life sciences, and most can only be solved approximately using computers. Numerical Analysis of Partial Differential Equations Using Maple and MATLAB provides detailed descriptions of the four major classes of discretization methods for PDEs (finite difference method, finite volume method, spectral method, and finite element method) and runnable MATLAB? code for each of the discretization methods and exercises. It also gives self-contained convergence proofs for each method using the tools and techniques required for the general convergence analysis but adapted to the simplest setting to keep the presentation clear and complete. This book is intended for advanced undergraduate and early graduate students in numerical analysis and scientific computing and researchers in related fields. It is appropriate for a course on numerical methods for partial differential equations.

Author : Matthew P. Coleman
Publisher : CRC Press
Page : 685 pages
File Size : 46,7 Mb
Release : 2013-06-26
Category : Mathematics
ISBN : 9781439898468

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An Introduction to Partial Differential Equations with MATLAB, Second Edition by Matthew P. Coleman Pdf

An Introduction to Partial Differential Equations with MATLAB®, Second Edition illustrates the usefulness of PDEs through numerous applications and helps students appreciate the beauty of the underlying mathematics. Updated throughout, this second edition of a bestseller shows students how PDEs can model diverse problems, including the flow of heat, the propagation of sound waves, the spread of algae along the ocean’s surface, the fluctuation in the price of a stock option, and the quantum mechanical behavior of a hydrogen atom. Suitable for a two-semester introduction to PDEs and Fourier series for mathematics, physics, and engineering students, the text teaches the equations based on method of solution. It provides both physical and mathematical motivation as much as possible. The author treats problems in one spatial dimension before dealing with those in higher dimensions. He covers PDEs on bounded domains and then on unbounded domains, introducing students to Fourier series early on in the text. Each chapter’s prelude explains what and why material is to be covered and considers the material in a historical setting. The text also contains many exercises, including standard ones and graphical problems using MATLAB. While the book can be used without MATLAB, instructors and students are encouraged to take advantage of MATLAB’s excellent graphics capabilities. The MATLAB code used to generate the tables and figures is available in an appendix and on the author’s website.

Author : Alain Vande Wouwer,Philippe Saucez,Carlos Vilas
Publisher : Springer
Page : 406 pages
File Size : 45,7 Mb
Release : 2014-06-07
Category : Technology & Engineering
ISBN : 9783319067902

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Simulation of ODE/PDE Models with MATLAB®, OCTAVE and SCILAB by Alain Vande Wouwer,Philippe Saucez,Carlos Vilas Pdf

Simulation of ODE/PDE Models with MATLAB®, OCTAVE and SCILAB shows the reader how to exploit a fuller array of numerical methods for the analysis of complex scientific and engineering systems than is conventionally employed. The book is dedicated to numerical simulation of distributed parameter systems described by mixed systems of algebraic equations, ordinary differential equations (ODEs) and partial differential equations (PDEs). Special attention is paid to the numerical method of lines (MOL), a popular approach to the solution of time-dependent PDEs, which proceeds in two basic steps: spatial discretization and time integration. Besides conventional finite-difference and element techniques, more advanced spatial-approximation methods are examined in some detail, including nonoscillatory schemes and adaptive-grid approaches. A MOL toolbox has been developed within MATLAB®/OCTAVE/SCILAB. In addition to a set of spatial approximations and time integrators, this toolbox includes a collection of application examples, in specific areas, which can serve as templates for developing new programs. Simulation of ODE/PDE Models with MATLAB®, OCTAVE and SCILAB provides a practical introduction to some advanced computational techniques for dynamic system simulation, supported by many worked examples in the text, and a collection of codes available for download from the book’s page at www.springer.com. This text is suitable for self-study by practicing scientists and engineers and as a final-year undergraduate course or at the graduate level.

Author : Cleve B. Moler
Publisher : SIAM
Page : 340 pages
File Size : 41,5 Mb
Release : 2010-08-12
Category : Computers
ISBN : 9780898716603

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Numerical Computing with MATLAB by Cleve B. Moler Pdf

A revised textbook for introductory courses in numerical methods, MATLAB and technical computing, which emphasises the use of mathematical software.

Author : Robert E. White
Publisher : CRC Press
Page : 403 pages
File Size : 43,5 Mb
Release : 2003-09-17
Category : Mathematics
ISBN : 9781135440329

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Computational Mathematics by Robert E. White Pdf

Computational Mathematics: Models, Methods, and Analysis with MATLAB and MPI explores and illustrates this process. Each section of the first six chapters is motivated by a specific application. The author applies a model, selects a numerical method, implements computer simulations, and assesses the ensuing results. These chapters include an abundance of MATLAB code. By studying the code instead of using it as a "black box, " you take the first step toward more sophisticated numerical modeling. The last four chapters focus on multiprocessing algorithms implemented using message passing interface (MPI). These chapters include Fortran 9x codes that illustrate the basic MPI subroutines and revisit the applications of the previous chapters from a parallel implementation perspective. All of the codes are available for download from www4.ncsu.edu./~white. This book is not just about math, not just about computing, and not just about applications, but about all three--in other words, computational science. Whether used as an undergraduate textbook, for self-study, or for reference, it builds the foundation you need to make numerical modeling and simulation integral parts of your investigational toolbox.

Author : Gabriel J. Lord,Catherine E. Powell,Tony Shardlow
Publisher : Cambridge University Press
Page : 0 pages
File Size : 46,5 Mb
Release : 2014-07-16
Category : Mathematics
ISBN : 1139898132

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An Introduction to Computational Stochastic PDEs by Gabriel J. Lord,Catherine E. Powell,Tony Shardlow Pdf

This book gives a comprehensive introduction to numerical methods and analysis of stochastic processes, random fields and stochastic differential equations, and offers graduate students and researchers powerful tools for understanding uncertainty quantification for risk analysis. Coverage includes traditional stochastic ODEs with white noise forcing, strong and weak approximation, and the multi-level Monte Carlo method. Later chapters apply the theory of random fields to the numerical solution of elliptic PDEs with correlated random data, discuss the Monte Carlo method, and introduce stochastic Galerkin finite-element methods. Finally, stochastic parabolic PDEs are developed. Assuming little previous exposure to probability and statistics, theory is developed in tandem with state-of the art computational methods through worked examples, exercises, theorems and proofs. The set of MATLAB codes included (and downloadable) allows readers to perform computations themselves and solve the test problems discussed. Practical examples are drawn from finance, mathematical biology, neuroscience, fluid flow modeling and materials science.

Author : Aslak Tveito,Ragnar Winther
Publisher : Springer Science & Business Media
Page : 392 pages
File Size : 50,6 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 : Ionut Danaila,Pascal Joly,Sidi Mahmoud Kaber,Marie Postel
Publisher : Springer Science & Business Media
Page : 294 pages
File Size : 43,5 Mb
Release : 2007-12-03
Category : Mathematics
ISBN : 9780387491592

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An Introduction to Scientific Computing by Ionut Danaila,Pascal Joly,Sidi Mahmoud Kaber,Marie Postel Pdf

This book demonstrates scientific computing by presenting twelve computational projects in several disciplines including Fluid Mechanics, Thermal Science, Computer Aided Design, Signal Processing and more. Each follows typical steps of scientific computing, from physical and mathematical description, to numerical formulation and programming and critical discussion of results. The text teaches practical methods not usually available in basic textbooks: numerical checking of accuracy, choice of boundary conditions, effective solving of linear systems, comparison to exact solutions and more. The final section of each project contains the solutions to proposed exercises and guides the reader in using the MATLAB scripts available online.

Author : William E. Schiesser,Graham W. Griffiths
Publisher : Cambridge University Press
Page : 491 pages
File Size : 42,6 Mb
Release : 2009-03-16
Category : Computers
ISBN : 9780521519861

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A Compendium of Partial Differential Equation Models by William E. Schiesser,Graham W. Griffiths Pdf

Presents numerical methods and computer code in Matlab for the solution of ODEs and PDEs with detailed line-by-line discussion.