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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.
Finite Difference Computing with Pdes by Andy Flair Pdf
An equation that relates to one or more functions with its derivatives is called a differential equation. A partial differential equation (PDE) is a type of differential equation, in which the equation consists of unknown multi variables with their partial derivatives. This is a special case of an ordinary differential equation. There is a large amount of modern mathematical and scientific research on methods for numerically approximating solutions of particular PDEs using computers. These are numerical methods for approximating the solutions to differential equations using finite difference equations to approximate derivatives. Finite difference computing is one of the most widely used methods for solving PDEs. This book outlines the processes and applications of finite difference computing with PDEs in detail. The topics included herein on finite difference computing with PDEs are of utmost significance and bound to provide incredible insights to readers. The book is appropriate for students seeking detailed information in this area as well as for experts.
Finite Difference Computing With PDEs by Hans Petter Langtangen,Svein Linge Pdf
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 by Hans Petter Langtangen,Svein Linge Pdf
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 Methods for Ordinary and Partial Differential Equations by Randall J. LeVeque Pdf
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 by J.W. Thomas Pdf
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 Gordon D. Smith Pdf
Substantially revised, this authoritative study covers the standard finite difference methods of parabolic, hyperbolic, and elliptic equations, and includes the concomitant theoretical work on consistency, stability, and convergence. The new edition includes revised and greatly expanded sections on stability based on the Lax-Richtmeyer definition, the application of Pade approximants to systems of ordinary differential equations for parabolic and hyperbolic equations, and a considerably improved presentation of iterative methods. A fast-paced introduction to numerical methods, this will be a useful volume for students of mathematics and engineering, and for postgraduates and professionals who need a clear, concise grounding in this discipline.
Numerical Solution of Partial Differential Equations by the Finite Element Method by Claes Johnson Pdf
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 Exponential Decay Models by Hans Petter Langtangen Pdf
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.
Numerical Methods for Partial Differential Equations by Sandip Mazumder Pdf
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
Numerical Partial Differential Equations: Finite Difference Methods by J.W. Thomas Pdf
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.
Finite Difference Computing: Theory and Software Applications by Adam Reid Pdf
Finite-difference methods (FDM) are a class of numerical techniques which are used for solving differential equations by estimating derivatives with finite differences. It involves discretizing the spatial domain and time interval. The value of the solution at these discrete points is approximated by solving algebraic equations having finite differences and values from adjacent points. Finite difference methods transform ordinary differential equations or partial differential equations, into a system of linear equations that can be solved by matrix algebra techniques. Modern computers can perform these linear algebra computations efficiently, which has led to the widespread use of FDM in modern numerical analysis. It is considered to be one of the most common approaches to the numerical solution of partial differential equations. This book is compiled in such a manner, that it will provide in-depth knowledge about the theory and practice of finite difference computing. Also included herein is a detailed explanation of the various concepts and applications of this method. Students, researchers, experts and all associated with finite-difference methods will benefit alike from this book.