Finite Difference Computing with Exponential Decay Models

1. Front Matter

   Pages i-xiv

   PDF

2. Algorithms and Implementations

   • Hans Petter Langtangen

   Pages 1-38Open Access

3. Analysis

   • Hans Petter Langtangen

   Pages 39-66Open Access

4. Generalizations

   • Hans Petter Langtangen

   Pages 67-89Open Access

5. Models

   • Hans Petter Langtangen

   Pages 91-125Open Access

6. Scientific Software Engineering

   • Hans Petter Langtangen

   Pages 127-187Open Access

7. Back Matter

   Pages 189-200

   PDF

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. 

• ordinary differential equations
• exponential decay models
• finite difference methods
• python programming
• software engineering

“This text provides an overview of the basics of scientific computing. … the author provides an excellent introduction to the field of scientific computing via a consideration of physically relevant models. … This text is an excellent tool for teaching and ideal for readers who would like to enter the field, or reinforce prior knowledge.” (Charis Harley, zbMATH 1356.65188, 2017)

• BioComp, Simula Research Laboratory BioComp, Lysaker, Norway

  Hans Petter Langtangen

Hans Petter Langtangen is a professor of computer science at the University of Oslo. He has formerly been a professor of mechanics and is now the director of a Norwegian Center of Excellence: "Center for Biomedical Computing", at Simula Research Laboratory. Langtangen has published over 100 scientific publications and written several books, including papers and a bestseller TCSE 6 "A Primer on Scientific Programming with Python", now in its 4th edition. He has also developed open source and commercial software systems for computational sciences.