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.