This course gives a broad introduction to numerical algorithms used in scientific computing. It covers classical methods to solve Ordinary and Partial Differential Equations such as spectral, finite difference and finite volume methods. A brief introduction to finite element methods is given. Explicit and implicit time integration using various high-order methods are discussed. We review basic methods to solve linear and non-linear systems of equations. Issues related to the implementation of efficient algorithms on modern high-performance computing systems are discussed. Hyperbolic systems of conservations laws are covered in detail.

Analysis of methods for the numerical solution of the partial differential equations of plasma physics, including those of elliptic, parabolic, hyperbolic, and eigenvalue type. Topics include finite difference, finite element, spectral, particle-in-cell, Monte Carlo, moving grid, and multiple-time-scale techniques, applied to the problems of plasma equilibrium, transport and stability. Basic parallel programming concepts are discussed.