Introduction to Numerical Solution of Differential Equations

Fundamental numerical techniques for solving ordinary and partial differential equations. Overview of techniques for approximation and integration of functions. Development of multi-step and multi-stage methods, error analysis, step-size control for ordinary differential equations. Solution of two-point boundary value problems, introduction to methods for solving linear partial differential equations. Students will be required to use MATLAB (or other computer languages) to implement the mathematical algorithms under consideration: experience with a programming language is therefore strongly recommended. Prerequisites: Multivariable calculus; Linear algebra; APMA 0355 or equivalent; APMA 0365 or equivalent.