Finite Difference Computing with PDEs
Title | Finite Difference Computing with PDEs PDF eBook |
Author | Hans Petter Langtangen |
Publisher | Springer |
Pages | 522 |
Release | 2017-06-21 |
Genre | Computers |
ISBN | 3319554565 |
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.
Finite Difference Methods for Ordinary and Partial Differential Equations
Title | Finite Difference Methods for Ordinary and Partial Differential Equations PDF eBook |
Author | Randall J. LeVeque |
Publisher | SIAM |
Pages | 356 |
Release | 2007-01-01 |
Genre | Mathematics |
ISBN | 9780898717839 |
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 Partial Differential Equations: Finite Difference Methods
Title | Numerical Partial Differential Equations: Finite Difference Methods PDF eBook |
Author | J.W. Thomas |
Publisher | Springer Science & Business Media |
Pages | 451 |
Release | 2013-12-01 |
Genre | Mathematics |
ISBN | 1489972781 |
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 Solution of Partial Differential Equations by the Finite Element Method
Title | Numerical Solution of Partial Differential Equations by the Finite Element Method PDF eBook |
Author | Claes Johnson |
Publisher | Courier Corporation |
Pages | 290 |
Release | 2012-05-23 |
Genre | Mathematics |
ISBN | 0486131599 |
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.
Finite Difference Computing With PDEs
Title | Finite Difference Computing With PDEs PDF eBook |
Author | Hans Petter Langtangen |
Publisher | |
Pages | 520 |
Release | 2020-10-08 |
Genre | Computers |
ISBN | 9781013268502 |
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. This work was published by Saint Philip Street Press pursuant to a Creative Commons license permitting commercial use. All rights not granted by the work's license are retained by the author or authors.
Finite Difference Computing with PDEs
Title | Finite Difference Computing with PDEs PDF eBook |
Author | Hans Petter Langtangen |
Publisher | Springer |
Pages | 610 |
Release | 2017-06-14 |
Genre | Computers |
ISBN | 9783319554556 |
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. This book is open access under a CC BY license.
Finite Difference Computing with Exponential Decay Models
Title | Finite Difference Computing with Exponential Decay Models PDF eBook |
Author | Hans Petter Langtangen |
Publisher | Springer |
Pages | 210 |
Release | 2016-06-10 |
Genre | Computers |
ISBN | 3319294393 |
This text provides a very simple, initial introduction to the complete scientific computing pipeline: models, discretization, algorithms, programming, verification, and visualization. The pedagogical strategy is to use one case study – an ordinary differential equation describing exponential decay processes – to illustrate fundamental concepts in mathematics and computer science. The book is easy to read and only requires a command of one-variable calculus and some very basic knowledge about computer programming. Contrary to similar texts on numerical methods and programming, this text has a much stronger focus on implementation and teaches testing and software engineering in particular.