MAT 544E - Numerical Analysis for Ordinary Differential Equations

Course Objectives

1. To introduce the basic concepts of the solutions of the ordinary differential equations and systems
2. To teach various numerical methods to solve ordinary differential equations.
3. To teach the general error analysis of various numerical methods.

Course Description

An introduction to the theory of differential equations. Stability of the initial value problem. Euler’s method. Error analysis and numerical stability for Euler’s method. Numerical methods for systems of differential equations. The backward Euler method and the trapezoidal method. Taylor and Runge-Kutta methods, their convergence, stability and asymptotic error. Multistep methods and general error analysis for multistep methods. Stiff differential equations. Implicit Runge-Kutta methods for stiff differential equations. Differential algebraic equations. Two-point boundary value problems.