AMSC/CMSC 667 Catalog Description

AMSC/CMSC 667, Numerical Analysis II (3 credits):
Numerical solution of initial value problems, numerical solution of boundary value problems, iterative methods for linear systems of equations, numerical methods for eigenvalue problems.

Details and Syllabi

Prerequisites

AMSC/CMSC 666 or equivalent background in numerics

Syllabus

Numerical Solution of Initial-Value Problems
- One-Step Methods, Runge-Kutta Methods
- Multistep Methods
- Consistency, Stability, and Convergence Analysis
- Error Estimation and Step Size Control
- Methods for Stiff Problems
Numerical Solution of Boundary-Value Problems
- Two-Point Boundary-Value Problems, Variational Formulations
- Finite Difference Methods: Consistency, Stability, and Convergence Analysis
- Finite Element Methods: Consistency, Stability, and Convergence Analysis
- Introduction to Error Estimation
- Multi-Dimensional Boundary-Value Problems
Iterative Methods for Linear Algebraic Systems
- Stationary Iterative Methods, Preconditioners
- Application to Multi-Dimensional Boundary-Value Problems
- Krylov Space Methods for Positive Definite Systems
- Krylov Space Methods for Indefinte Symmetric Systems
- Krylov Space Methods for Nonsymmetric Systems
- Multigrid Methods
Numerical Methods for Eigenvalue Problems
- Normal Forms, Rayleigh Quotients, and Singular Value Decompositions
- Power and Inverse Power Methods, QR Algorithms
- Lanczos and Arnoldi Methods