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Finite Difference Computing with Exponential Decay Models

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Book Series: Lecture Notes in Computational Science and Engineering ISSN: 1439-7358 ISBN: 9783319294384 9783319294391 Year: Volume: 110 Pages: 200 DOI: 10.1007/978-3-319-29439-1 Language: English
Publisher: Springer Nature
Subject: Computer Science --- Mathematics
Added to DOAB on : 2017-01-24 17:39:00
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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.

Programming for Computations - Python: A Gentle Introduction to Numerical Simulations with Python

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Book Series: Texts in Computational Science and Engineering ISSN: 1611-0994 ISBN: 9783319324272 9783319324289 Volume: 15 Pages: 232 DOI: 10.1007/978-3-319-32428-9 Language: English
Publisher: Springer Nature
Subject: Computer Science
Added to DOAB on : 2017-02-03 18:19:48
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Numerical simulations;programming;Python

Programming for Computations - MATLAB/Octave

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Book Series: Texts in Computational Science and Engineering ISSN: 1611-0994 ISBN: 9783319324517 9783319324524 Year: Volume: 14 Pages: 216 DOI: 10.1007/978-3-319-32452-4 Language: English
Publisher: Springer Nature
Subject: Computer Science
Added to DOAB on : 2017-02-03 18:31:09
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This book presents computer programming as a key method for solving mathematical problems. There are two versions of the book, one for MATLAB and one for Python. The book was inspired by the Springer book TCSE 6: A Primer on Scientific Programming with Python (by Langtangen), but the style is more accessible and concise, in keeping with the needs of engineering students. The book outlines the shortest possible path from no previous experience with programming to a set of skills that allows the students to write simple programs for solving common mathematical problems with numerical methods in engineering and science courses. The emphasis is on generic algorithms, clean design of programs, use of functions, and automatic tests for verification.

Solving PDEs in Python: The FEniCS Tutorial I

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Book Series: Simula SpringerBriefs on Computing ISBN: 9783319524610 9783319524627 Year: DOI: 10.1007/978-3-319-52462-7 Language: English
Publisher: Springer Nature
Subject: Computer Science
Added to DOAB on : 2017-04-11 12:12:58
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This book offers a concise and gentle introduction to finite element programming in Python based on the popular FEniCS software library. Using a series of examples, including the Poisson equation, the equations of linear elasticity, the incompressible Navier–Stokes equations, and systems of nonlinear advection–diffusion–reaction equations, it guides readers through the essential steps to quickly solving a PDE in FEniCS, such as how to define a finite variational problem, how to set boundary conditions, how to solve linear and nonlinear systems, and how to visualize solutions and structure finite element Python programs.

Finite Difference Computing with PDEs: A Modern Software Approach

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Book Series: Texts in Computational Science and Engineering ISSN: 1611-0994 / 2197-179X ISBN: 9783319554556 9783319554563 Year: Pages: 507 DOI: https://doi.org/10.1007/978-3-319-55456-3 Language: English
Publisher: Springer Nature
Subject: Computer Science
Added to DOAB on : 2017-11-24 13:03:18
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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

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Book Series: Simula SpringerBriefs on Computing ISBN: 9783319327259 9783319327266 Year: Pages: 138 DOI: 10.1007/978-3-319-32726-6 Language: English
Publisher: Springer Nature
Subject: Mathematics
Added to DOAB on : 2017-01-24 17:59:55
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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.

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