Finite Difference Computing with Exponential Decay Models - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Finite Difference Computing with Exponential Decay Models write by Hans Petter Langtangen. This book was released on 2016-06-10. Finite Difference Computing with Exponential Decay Models available in PDF, EPUB and Kindle. 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.
Finite Difference Computing with PDEs
Finite Difference Computing with PDEs - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Finite Difference Computing with PDEs write by Hans Petter Langtangen. This book was released on 2017-06-21. Finite Difference Computing with PDEs available in PDF, EPUB and Kindle. 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.
Scaling of Differential Equations
Scaling of Differential Equations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Scaling of Differential Equations write by Hans Petter Langtangen. This book was released on 2016-06-15. Scaling of Differential Equations available in PDF, EPUB and Kindle. The book serves both as a reference for various scaled models with corresponding dimensionless numbers, and as a resource for learning the art of scaling. A special feature of the book is the emphasis on how to create software for scaled models, based on existing software for unscaled models. Scaling (or non-dimensionalization) is a mathematical technique that greatly simplifies the setting of input parameters in numerical simulations. Moreover, scaling enhances the understanding of how different physical processes interact in a differential equation model. Compared to the existing literature, where the topic of scaling is frequently encountered, but very often in only a brief and shallow setting, the present book gives much more thorough explanations of how to reason about finding the right scales. This process is highly problem dependent, and therefore the book features a lot of worked examples, from very simple ODEs to systems of PDEs, especially from fluid mechanics. The text is easily accessible and example-driven. The first part on ODEs fits even a lower undergraduate level, while the most advanced multiphysics fluid mechanics examples target the graduate level. The scientific literature is full of scaled models, but in most of the cases, the scales are just stated without thorough mathematical reasoning. This book explains how the scales are found mathematically. This book will be a valuable read for anyone doing numerical simulations based on ordinary or partial differential equations.
Introduction to Numerical Methods for Variational Problems
Introduction to Numerical Methods for Variational Problems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Introduction to Numerical Methods for Variational Problems write by Hans Petter Langtangen. This book was released on 2019-09-26. Introduction to Numerical Methods for Variational Problems available in PDF, EPUB and Kindle. This textbook teaches finite element methods from a computational point of view. It focuses on how to develop flexible computer programs with Python, a programming language in which a combination of symbolic and numerical tools is used to achieve an explicit and practical derivation of finite element algorithms. The finite element library FEniCS is used throughout the book, but the content is provided in sufficient detail to ensure that students with less mathematical background or mixed programming-language experience will equally benefit. All program examples are available on the Internet.
Scientific Computing
Scientific Computing - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Scientific Computing write by John A. Trangenstein. This book was released on 2018-05-14. Scientific Computing available in PDF, EPUB and Kindle. This is the second of three volumes providing a comprehensive presentation of the fundamentals of scientific computing. This volume discusses more advanced topics than volume one, and is largely not a prerequisite for volume three. This book and its companions show how to determine the quality of computational results, and how to measure the relative efficiency of competing methods. Readers learn how to determine the maximum attainable accuracy of algorithms, and how to select the best method for computing problems. This book also discusses programming in several languages, including C++, Fortran and MATLAB. There are 49 examples, 110 exercises, 66 algorithms, 24 interactive JavaScript programs, 77 references to software programs and 1 case study. Topics are introduced with goals, literature references and links to public software. There are descriptions of the current algorithms in LAPACK, GSLIB and MATLAB. This book could be used for a second course in numerical methods, for either upper level undergraduates or first year graduate students. Parts of the text could be used for specialized courses, such as nonlinear optimization or iterative linear algebra.
