Jaun A. Numerical methods for partial differential equations

Royal Institute of Technology, 1999. — 81 p.
This is the first web edition of a course taught 1997-1999 at the Royal Institute of Technology (KTH, Stockholm) to graduate students in physics, engineering and quantitative social sciences. Realizing the need of an introductory text giving a comparative overview of a variety of methods commonly used to solve partial differential equations, and more than ever convinced that numerical techniques are best illustrated directly with a computer, new tools for the electronic publishing have been used to create a highly interactive document. Following hyper-links from the lecture
notes directly into the relevant sections of the program and executing the JBONE applet in the web page with different parameters and initial conditions, it is now possible to illustrate every step from the formulation of a problem, the discretization, until the final properties of numerical
schemes, with practical examples. Comparisons show what are the advantages and drawbacks of different approaches, which are generally treated separately in more advanced and specialized books. As a by-product of this new approach of teaching, students rapidly acquired the knowledge
for the electronic publishing of their home assignments and learned how to interact and help each other with newsgroups — two very useful tools when the research is carried out in international collaborations. The complete source of the JBONE Java program can be obtained free of charge
for personal use by sending an e-mail request to jaun@fusion.kth.se. For this web edition immediately accessible to everyone on the internet, I would like first to thank Kurt Appert (EPFL, Lausanne) for the inspiration and guidance he provided ever since I became a student of his own course Experimentation Numerique. Johan Carlsson, Johan Hedin and Thomas Jonsson (KTH, Stockholm) have one after the other been responsible for the Monte-Carlo method, Johan Hedin providing everyone of us with rapid and very competent advice in a sophisticated, geographically distributed, multi-platform environment. Ambrogio Fasoli (MIT, Cambridge), with whom I have the pleasure to collaborate for research by comparing numerical solutions of PDEs with experiments, carried out the measurement of Alfven instabilities illustrating how important aliasing can be for the digital data acquisition. I am finally greatful for the suggestions, criticisms and encouragements from the students, who will keep on forging the course as it evolves in the
future.