Computational Partial Differential Equations
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Computational Partial Differential Equations Using Matlab
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Author : Jichun Li
language : en
Publisher: CRC Press
Release Date : 2019-09-26
Computational Partial Differential Equations Using Matlab written by Jichun Li and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-26 with Mathematics categories.
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.
Computational Partial Differential Equations Using Matlab
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Author : Jichun Li
language : en
Publisher: CRC Press
Release Date : 2008-10-20
Computational Partial Differential Equations Using Matlab written by Jichun Li and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-10-20 with Mathematics categories.
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
Advanced Topics In Computational Partial Differential Equations
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Author : Hans Petter Langtangen
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-09-22
Advanced Topics In Computational Partial Differential Equations written by Hans Petter Langtangen 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 2012-09-22 with Mathematics categories.
This book is about solving partial differential equations (PDEs). Such equa tions are used to model a wide range ofphenomena in virtually all fields ofsci ence and technology. Inthe last decade, the general availability of extremely powerful computers has shifted the focus in computational mathematics from simplified model problems to much more sophisticated models resembling in tricate features of real life. This change challenges our knowledge in computer science and in numerical analysis. The main objective ofthe present book is to teach modern,advanced tech niques for numerical PDE solution. The book also introduces several models arising in fields likefinance, medicine, material technology, and geology. Inor der to read this book, you must have a basic knowledge of partial differential equations and numerical methods for solving such equations. Furthermore, some background in finite element methods is required. You do not need to know Diffpack, although this programming environment is used in examples throughout the text. Basically, this book is about models, methods, and how to implement the methods. For the implementation part it is natural for us to use Diffpack as the programming environment, because making a PDE solver in Diffpack requires little amount of programming and because Diff pack has support for the advanced numerical methods treated in this book. Most chapters have a part on models and methods, and a part on imple mentation and Diffpack programming. The exposition is designed such that readers can focus only on the first part, if desired.
Computational Differential Equations
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Author : Kenneth Eriksson
language : en
Publisher: Cambridge University Press
Release Date : 1996-09-05
Computational Differential Equations written by Kenneth Eriksson 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 1996-09-05 with Mathematics categories.
This textbook on computational mathematics is based on a fusion of mathematical analysis, numerical computation and applications.
Essential Partial Differential Equations
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Author : David F. Griffiths
language : en
Publisher: Springer
Release Date : 2015-09-24
Essential Partial Differential Equations written by David F. Griffiths and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-09-24 with Mathematics categories.
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.
Numerical Approximation Of Partial Differential Equations
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Author : Alfio Quarteroni
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-02-11
Numerical Approximation Of Partial Differential Equations written by Alfio Quarteroni 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 2009-02-11 with Mathematics categories.
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).
Numerical Methods For Nonlinear Partial Differential Equations
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Author : Sören Bartels
language : en
Publisher: Springer
Release Date : 2015-01-19
Numerical Methods For Nonlinear Partial Differential Equations written by Sören Bartels and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-01-19 with Mathematics categories.
The description of many interesting phenomena in science and engineering leads to infinite-dimensional minimization or evolution problems that define nonlinear partial differential equations. While the development and analysis of numerical methods for linear partial differential equations is nearly complete, only few results are available in the case of nonlinear equations. This monograph devises numerical methods for nonlinear model problems arising in the mathematical description of phase transitions, large bending problems, image processing, and inelastic material behavior. For each of these problems the underlying mathematical model is discussed, the essential analytical properties are explained, and the proposed numerical method is rigorously analyzed. The practicality of the algorithms is illustrated by means of short implementations.
Numerical Methods For Evolutionary Differential Equations
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Author : Uri M. Ascher
language : en
Publisher: SIAM
Release Date : 2008-09-04
Numerical Methods For Evolutionary Differential Equations written by Uri M. Ascher and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-09-04 with Mathematics categories.
Develops, analyses, and applies numerical methods for evolutionary, or time-dependent, differential problems.
Mathematical And Numerical Methods For Partial Differential Equations
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Author : Joël Chaskalovic
language : en
Publisher: Springer
Release Date : 2014-05-16
Mathematical And Numerical Methods For Partial Differential Equations written by Joël Chaskalovic and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-16 with Mathematics categories.
This self-tutorial offers a concise yet thorough introduction into the mathematical analysis of approximation methods for partial differential equation. A particular emphasis is put on finite element methods. The unique approach first summarizes and outlines the finite-element mathematics in general and then in the second and major part, formulates problem examples that clearly demonstrate the techniques of functional analysis via numerous and diverse exercises. The solutions of the problems are given directly afterwards. Using this approach, the author motivates and encourages the reader to actively acquire the knowledge of finite- element methods instead of passively absorbing the material as in most standard textbooks. This English edition is based on the Finite Element Methods for Engineering Sciences by Joel Chaskalovic.
Numerical Partial Differential Equations In Finance Explained
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Author : Karel in 't Hout
language : en
Publisher: Springer
Release Date : 2017-09-02
Numerical Partial Differential Equations In Finance Explained written by Karel in 't Hout and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-02 with Business & Economics categories.
This book provides a first, basic introduction into the valuation of financial options via the numerical solution of partial differential equations (PDEs). It provides readers with an easily accessible text explaining main concepts, models, methods and results that arise in this approach. In keeping with the series style, emphasis is placed on intuition as opposed to full rigor, and a relatively basic understanding of mathematics is sufficient. The book provides a wealth of examples, and ample numerical experiments are givento illustrate the theory. The main focus is on one-dimensional financial PDEs, notably the Black-Scholes equation. The book concludes with a detailed discussion of the important step towards two-dimensional PDEs in finance.