Computational modelling is an essential tool in Astrophysics and Geophysics. Comprehension of diverse physical effects including fluid and gas flow under gravity, heat and radiation transport, oscillations and seismology, formation of structures in the universe etc. is being developed through computations. This course aims to introduce the students to some of the basic techniques to perform such computational modelling. At the heart of the mathematical description of these problems are partial differential equations (PDEs). Several common numerical methods used to solve PDEs are introduced, with application examples drawn from Astrophysical and Geophysical settings. Methods of inference from observational data are also discussed, along with techniques of Monte-Carlo simulations.
Pre-requisites: Familiarity with coding and calculus; basic knowledge of classical mechanics and thermodynamics.
1. Numerical Recipes: The Art of Scientific Computing - by W.H. Press, S.A. Teukolsky, W.T. Vetterling and B.P. Flannery, Cambridge University Press, http://numerical.recipes
2. Finite Volume Methods for Hyperbolic Problems - by Randall J. Leveque, Cambridge University Press
3. Numerical Solutions of Partial Differential Equations - by K.W. Morton and D.F. Mayers, Cambridge University Press
4. Partial Differential Equations for Scientists and Engineers - by Stanley F. Farlow, Dover Publications
5. Lecture Notes on Computational Geophysics by A.P. van den Berg: http:// www.geo.uu.nl/~berg/compgeoph/lecturenotes.pdf