Syllabus for Numerical Methods II, to be taught in the spring semester

Nonlinear equations (Newton's method). Ordinary differential equations: initial value problem (Runge-Kutta and multistep methods, convergence and stability); two-point boundary value problem. Elliptic partial differential equations: finite difference and finite element methods, fast solvers, multigrid, iterative methods exploiting special structure. Brief introduction to time dependent partial differential equations. Current software packages. Computer programming assignments form an essential part of the course.