AMCS 252 Num. Analysis of Differential Equations



Theory and technique for the numerical analysis of ODEs and of PDEs of parabolic, hyperbolic, and elliptic type: accuracy, stability,convergence and qualitative properties. Runge-Kutta and linear multistep methods, zero-stability, absolute stability,stiffness, and order conditions. Finite difference methods, multigrid, dimensional and perator splitting, and the CFL condition. The course covers theory and algorithms for the numerical solution of ODEs and of PDEs of parabolic, hyperbolic, and elliptic type. Theoretical concepts include: accuracy, zero-stability, absolute stability, convergence, order of accuracy, stiffness, conservation, and the CFL condition. Algorithms covered include: finite differences, steady and unsteady discretization in one (1)and two (2) dimensions, Newton methods, Runge-Kutta methods, linear multistep methods, multigrid, implicit methods for stiff problems, centered and upwind methods for wave equations, dimensional splitting and operator splitting. AMCS 252 was previously entitled "Numerical Analysis of PDEs" during Springs of 2011 and 2012.
Course period02/5/11 → …
Course level200