PH 206

Computational Physics

2-0-2-6

 

Syllabus:

Solutions of Algebraic and Transcendental Equations: Bisection methods, Interpolation methods, Iterative methods.

Matrices: System of linear equations, Gauss and Gauss-Jordan elimination, Matrix Inversion, LU decomposition, Eigen value and eigenvector problems, Power and Jacobi method, application to physics problems;

Interpolation: Newton's divided difference method; Linear and nonlinear least squares fitting;

Numerical Differentiation; Numerical integration: Newton–Cotes formulae, Gauss Quadrature;

Ordinary and Partial Differential Equations: Euler, Runge-Kutta and finite difference methods; solution to initial and boundary value problems, Finite difference solutions to hyperbolic, parabolic and elliptic partial differential equations, application to physics problems;

Monte Carlo Simulation: Markov process and Markov chain, random numbers, simple and importance sampling, Metropolis algorithm, 2D- Ising model.

Texts:

  1. S. S. M. Wong, Computational Methods in Physics and Engineering, World Scientific, 1997.
  2. T. Pang, An Introduction to Computational Physics, Cambridge University Press, 1997.

References:

  1. R. H. Landau, M. J. Paez and C. C. Bordeianu, Computational Physics: Problem Solving with Computer, Wiley VchVerlagGmbh& Co. KGaA, 2007.

  2. D. Frenkel and B. Smit, Understanding Molecular Simulation, Academic Press, 1996.

  3. M. E. J. Newman and G. T. Barkema, Monte Carlo Methods in Statistical Physics, Clarendon Press, Oxford, 2001.
  4. M. P. Allen and D. J. Tildesley, Computer Simulation of Liquids, Clarendon Press, Oxford, 1991.

  5. W. H. Press, S. A. Teukolsky, W. T. Verlling and B. P. Flannery, Numerical Recipes in C/Fortran, Cambridge, 1998.