# Numerical Solution of Ordinary Differential Equations Matlab Component

This page contains links to the hand-outs, problem sheets and designed for a Matlab practical on numerical methods for ordinary differential equations held in the 99/00 autumn semester at Brunel University.

## Handouts Organisational Information Guide: "How to use Matlab" Problem Sheet 1 Assignment 1 Problem Sheet 2 Assignment 2

## Solutions to Problem Sheets/Assignments

### Solutions to Problem Sheet 1 Euler_One_Step.m Euler.m test_Euler.m better_Euler.m test_better_Euler.m

### Solutions to Assignment 1

#### Problem 1 Euler_One_Step2.m f_example.m Testing of Euler_One_Step2

#### Problem 2 new_Euler.m f_ex2.m M-file to test new_Euler

#### Problem 3 The required M-file (also includes instructions for Problem 4)

#### Problem 4 Runge3_One_Step.m Runge_Kutta3.m The required M-file

### Solutions to Problem Sheet 2 Euler_Step_Sys.m Euler_Sys.m Test file for Problem 2: test_Euler_Sys.m Implementation of function f : f_prob2.m Implementation of function g : g_prob2.m

### Solutions to Assignment 2

#### Problem 1 Runge3_Step_Sys.m, a function called by Runge_Kutta3_Sys Runge_Kutta3_Sys.m Implementation of function f : f_prob2.m Implementation of function g : g_prob2.m M-file to test Runge_Kutta3_Sys

#### Problem 2 Implementation of function f : f_a2p2.m Implementation of function g : g_a2p2.m M-file to compute and plot the maximum relative errors
The answer to the final question is, that the relative error is approximately divided by eight if the number of mesh points is doubled. This is the expected behaviour of a third order method.

#### Problem 3 Implementation of function f : f_a2p3.m Implementation of function g : g_a2p3.m M-file to compute the height of the spear plot of the different flight-paths (post-script)