Finite Difference Computing with Exponential Decay Models.

• Superior document: Lecture Notes in Computational Science and Engineering Series ; v.110
• Author: Langtangen, Hans Petter.
• Place / Publishing House: Cham : : Springer International Publishing AG,, 2016.; Ã2016.
• Year of Publication: 2016
• Edition: 1st ed.
• Language: English
• Series: Lecture Notes in Computational Science and Engineering Series
• Physical Description: 1 online resource (210 pages)

Table of Contents

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.