Introductory Finite Volume Methods for PDEs
Author :
Publisher : Bookboon
Page : 82 pages
File Size : 10,23 MB
Release :
Category :
ISBN : 8776818829
Numerical Methods for Partial Differential Equations
Author : Vitoriano Ruas
Publisher : John Wiley & Sons
Page : 376 pages
File Size : 37,59 MB
Release : 2016-04-28
Category : Technology & Engineering
ISBN : 1119111366
Book Description
Numerical Methods for Partial Differential Equations: An Introduction Vitoriano Ruas, Sorbonne Universités, UPMC - Université Paris 6, France A comprehensive overview of techniques for the computational solution of PDE's Numerical Methods for Partial Differential Equations: An Introduction covers the three most popular methods for solving partial differential equations: the finite difference method, the finite element method and the finite volume method. The book combines clear descriptions of the three methods, their reliability, and practical implementation aspects. Justifications for why numerical methods for the main classes of PDE's work or not, or how well they work, are supplied and exemplified. Aimed primarily at students of Engineering, Mathematics, Computer Science, Physics and Chemistry among others this book offers a substantial insight into the principles numerical methods in this class of problems are based upon. The book can also be used as a reference for research work on numerical methods for PDE’s. Key features: A balanced emphasis is given to both practical considerations and a rigorous mathematical treatment The reliability analyses for the three methods are carried out in a unified framework and in a structured and visible manner, for the basic types of PDE's Special attention is given to low order methods, as practitioner's overwhelming default options for everyday use New techniques are employed to derive known results, thereby simplifying their proof Supplementary material is available from a companion website.
Numerical Methods for Partial Differential Equations
Author : Sandip Mazumder
Publisher : Academic Press
Page : 484 pages
File Size : 36,67 MB
Release : 2015-12-01
Category : Mathematics
ISBN : 0128035048
Book Description
Numerical Methods for Partial Differential Equations: Finite Difference and Finite Volume Methods focuses on two popular deterministic methods for solving partial differential equations (PDEs), namely finite difference and finite volume methods. The solution of PDEs can be very challenging, depending on the type of equation, the number of independent variables, the boundary, and initial conditions, and other factors. These two methods have been traditionally used to solve problems involving fluid flow. For practical reasons, the finite element method, used more often for solving problems in solid mechanics, and covered extensively in various other texts, has been excluded. The book is intended for beginning graduate students and early career professionals, although advanced undergraduate students may find it equally useful. The material is meant to serve as a prerequisite for students who might go on to take additional courses in computational mechanics, computational fluid dynamics, or computational electromagnetics. The notations, language, and technical jargon used in the book can be easily understood by scientists and engineers who may not have had graduate-level applied mathematics or computer science courses. - Presents one of the few available resources that comprehensively describes and demonstrates the finite volume method for unstructured mesh used frequently by practicing code developers in industry - Includes step-by-step algorithms and code snippets in each chapter that enables the reader to make the transition from equations on the page to working codes - Includes 51 worked out examples that comprehensively demonstrate important mathematical steps, algorithms, and coding practices required to numerically solve PDEs, as well as how to interpret the results from both physical and mathematic perspectives
Finite Volume Methods for Hyperbolic Problems
Author : Randall J. LeVeque
Publisher : Cambridge University Press
Page : 582 pages
File Size : 42,83 MB
Release : 2002-08-26
Category : Mathematics
ISBN : 1139434187
Book Description
This book, first published in 2002, contains an introduction to hyperbolic partial differential equations and a powerful class of numerical methods for approximating their solution, including both linear problems and nonlinear conservation laws. These equations describe a wide range of wave propagation and transport phenomena arising in nearly every scientific and engineering discipline. Several applications are described in a self-contained manner, along with much of the mathematical theory of hyperbolic problems. High-resolution versions of Godunov's method are developed, in which Riemann problems are solved to determine the local wave structure and limiters are then applied to eliminate numerical oscillations. These methods were originally designed to capture shock waves accurately, but are also useful tools for studying linear wave-propagation problems, particularly in heterogenous material. The methods studied are implemented in the CLAWPACK software package and source code for all the examples presented can be found on the web, along with animations of many of the simulations. This provides an excellent learning environment for understanding wave propagation phenomena and finite volume methods.
Finite Difference Methods for Ordinary and Partial Differential Equations
Author : Randall J. LeVeque
Publisher : SIAM
Page : 356 pages
File Size : 33,88 MB
Release : 2007-01-01
Category : Mathematics
ISBN : 9780898717839
Book Description
This book introduces finite difference methods for both ordinary differential equations (ODEs) and partial differential equations (PDEs) and discusses the similarities and differences between algorithm design and stability analysis for different types of equations. A unified view of stability theory for ODEs and PDEs is presented, and the interplay between ODE and PDE analysis is stressed. The text emphasizes standard classical methods, but several newer approaches also are introduced and are described in the context of simple motivating examples.
Numerical Solution of Partial Differential Equations by the Finite Element Method
Author : Claes Johnson
Publisher : Courier Corporation
Page : 290 pages
File Size : 35,2 MB
Release : 2012-05-23
Category : Mathematics
ISBN : 0486131599
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.
Numerical Solution of Differential Equations
Author : Zhilin Li
Publisher : Cambridge University Press
Page : 305 pages
File Size : 23,34 MB
Release : 2017-11-30
Category : Mathematics
ISBN : 1107163226
Book Description
A practical and concise guide to finite difference and finite element methods. Well-tested MATLAB® codes are available online.
Introductory Finite Difference Methods for PDEs
Author :
Publisher : Bookboon
Page : 144 pages
File Size : 13,34 MB
Release :
Category :
ISBN : 8776816427
Book Description
Numerical Partial Differential Equations: Finite Difference Methods
Author : J.W. Thomas
Publisher : Springer Science & Business Media
Page : 451 pages
File Size : 24,2 MB
Release : 2013-12-01
Category : Mathematics
ISBN : 1489972781
Book Description
What makes this book stand out from the competition is that it is more computational. Once done with both volumes, readers will have the tools to attack a wider variety of problems than those worked out in the competitors' books. The author stresses the use of technology throughout the text, allowing students to utilize it as much as possible.
Numerical Methods for Solving Partial Differential Equations
Author : George F. Pinder
Publisher : John Wiley & Sons
Page : 414 pages
File Size : 22,60 MB
Release : 2018-02-05
Category : Technology & Engineering
ISBN : 1119316383
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.
