$$ \newcommand{\D}{\displaystyle} \renewcommand{\eqref}[1]{Eq.~(\ref{#1})} $$




1 Preliminaries

1.1 Acknowledgements and dedications

This digital compendium is based on the compendium Numeriske Beregninger by my good friend and colleague Jan B. Aarseth who shared all of his work so generously and willingly. His compendium served as an excellent basis for further development and modernisation in terms of accessibility on the web, programming language, and naturally numerous theoretical extensions and removals. Primarily, the digital compendium is intended to be used in the course TKT-4140 Numerical Methods at NTNU.

The development of the technical solutions for this digital compendium results from collaborations with professor Hans Petter Langtangen, who has developed Doconce for flexible typesetting, and associate professor Hallvard Trætteberg at IDI, NTNU, who has developed the webpage-parser which identifies and downloads Python-code from webpages for integration in Eclipse IDEs. The the development of the digital compendium has been funded by the project IKTiSU. and NTNU Teaching Excellense 2015-2016.

Johan Kolstø Sønstabø was instrumental in the initial phase and the development of the first version of the Digital Compendium consisting of only Chapter 1 and for programming examples and development of exercises.

Fredrik Eikeland Fossan has contributed enormously by implementing python codes for most chapters. In particular, his contributions to the test procedures for MMS and to algorithms for testing of the order of accuracy of numerical schemes are highly appreciated.

Lucas Omar Müller taught the course TKT 4140 in the spring semester 2017. Apart from doing an excellent job in teaching by bringing in a wide range of new elements, he has also made numerous contributions in translating the compendium from Norwegian to English and by adding theoretical sections.

Marie Kjeldsen Bergvoll made important contributions during her summer-job with the translation of chapters 2-7 from LaTeX to Doconce. Tragically, Marie passed away due to a sudden illness while being in China working on her master thesis in March 2017. Her choice of courses were motivated by interest, curiousity and a hunger for knowledge. The very same mentality brought her to countries like Germany and China, where English is not the official language. She was a energetic, independent, warm, and dedicated young student, with good analytical skills and a talent for mathematics.

Hans Petter Langtangen, passed away on October 10th in 2016. Hans Petter was an extraordinarily productive author, lecturer, supervisor and researcher. His books on software and methods for solving differential equations are widely used and have influenced these fields considerably. Ever since I meet Hans Petter for the first time, when he acted as my opponent at my PhD-defense in 1999 and later on as a collaborator at CBC, I have learned to know him as an enthusiastic and playful scholar with a great passion for science. He was truly a unique character in our field. Who else would write his own flexible markup language producing output to a range of web-formats and PDF, before setting off to produce piles of textbooks? But maybe even more important was his inspirational, energetic and natural ways of interaction with friends, colleagues, and collaborators in a great variety of disciplines. I miss him dearly both as a friend and collaborator.

During the work with this digital compendium, we have suffered the loss of Hans Petter and Marie, two fantastic but quite different persons. Hans Petter at the full bloom of his career, whereas Marie was a talented, young master student, just about to start her career.

To honor the memories of both Hans Petter and Marie, I dedicate this digital compendium to them.

Leif Rune Hellevik

Trondheim, October 19, 2017.