Finite Difference Computing with Exponential Decay Models

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 p...

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Hlavní autor: Langtangen, Hans Petter
Médium: E-kniha Kniha
Jazyk:angličtina
Vydáno: Cham Springer Nature 2016
Springer Open
Springer International Publishing AG
SpringerOpen
Vydání:1
Edice:Lecture Notes in Computational Science and Engineering
Témata:
Computational Science and Engineering
Computer Engineering
Computer science
Computer science > Mathematics
Computers
Computing and Information Technology
Data processing Computer science
Finite differences
Mathematics
Mathematics and Science
Programming Techniques
software Engineering
ISBN:9783319294391, 3319294393, 9783319294384, 3319294385, 9783319485140, 3319485148, 9783319485133, 331948513X
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Abstract 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.
AbstractList Computational Science and Engineering; software Engineering; Programming Techniques
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.
Author Langtangen, Hans Petter
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Notes Includes bibliographical references (p. 189) and index
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Snippet Computational Science and Engineering; software Engineering; Programming Techniques
This text provides a very simple, initial introduction to the complete scientific computing pipeline: models, discretization, algorithms, programming,...
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SubjectTerms Computational Science and Engineering
Computer Engineering
Computer science
Computer science -- Mathematics
Computers
Computing and Information Technology
Data processing Computer science
Finite differences
Mathematics
Mathematics and Science
Programming Techniques
software Engineering
TableOfContents Intro -- Preface -- Contents -- List of Exercises, Problems, and Projects -- 1 Algorithms and Implementations -- 1.1 Finite Difference Methods -- 1.2 Implementations -- 1.3 Exercises -- 2 Analysis -- 2.1 Experimental Investigations -- 2.2 Stability -- 2.3 Accuracy -- 2.4 Various Types of Errors in a Differential Equation Model -- 2.5 Exercises -- 3 Generalizations -- 3.1 Model Extensions -- 3.2 General First-Order ODEs -- 3.3 Exercises -- 4 Models -- 4.1 Scaling -- 4.2 Evolution of a Population -- 4.3 Compound Interest and Inflation -- 4.4 Newton's Law of Cooling -- 4.5 Radioactive Decay -- 4.6 Chemical Kinetics -- 4.7 Spreading of Diseases -- 4.8 Predator-Prey Models in Ecology -- 4.9 Decay of Atmospheric Pressure with Altitude -- 4.10 Compaction of Sediments -- 4.11 Vertical Motion of a Body in a Viscous Fluid -- 4.12 Viscoelastic Materials -- 4.13 Decay ODEs from Solving a PDE by Fourier Expansions -- 4.14 Exercises -- 5 Scientific Software Engineering -- 5.1 Implementations with Functions and Modules -- 5.2 User Interfaces -- 5.3 Tests for Verifying Implementations -- 5.4 Sharing the Software with Other Users -- 5.5 Classes for Problem and Solution Method -- 5.6 Automating Scientific Experiments -- 5.7 Exercises -- References -- Index
Title Finite Difference Computing with Exponential Decay Models
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