Matematik och Datavetenskap, Chalmers Tekniska Högskola och Göteborgs Universitet

TMA740B Analys i en variabel Kf Kb, del B, 1999, vecka 5

Mathematics

Goal: Differential equations.

Theory: Read Chapter 32 "Autonomous scalar initial value problem", Chapter 33 "Separable scalar initial value problems", and Chapter 34 "The general initial value problem".

Exercises: Basic: 32.1, 32.1, 32.3, 32.4, 33.1, 33.3
Additional problems for chapters 32-34
Advanced: 33.2, 33.4

Project: Instructions for the project.

Programming

Goal: To write a matlab function that computes the solution of the general initial value problem.

Try matlab's editor. You may like it better than emacs. To open the file funk1.m you type "edit funk1" in the matlab command window.

Exercises:

1. Write a matlab function that implements the Euler forward method in Section 34.6 for the system of equations u'=f(u,x).

The program should be written according to the specification in the skeleton my_ode.m.

2. Test your program on a differential equation for which you know the exact solution. Compute the error for stepsizes h=.1, .01, .001. Explain. Compare with matlab's ode23.

3. Solve several systems of equations from chapters 32-34. In each case plot both
    solution curves:     >> plot(t,u)
    phase portrait:       >> plot( u(:,1), u(:,2) )

Individual report

In the beginning of week 5 each student should report (in any suitable form, e.g., a short discussion in front of the blackboard or the computer) to her/his supervisor the following:
1. problem 34.8
2. my_ode

/stig


Last modified: Sun Nov 21 23:55:20 MET 1999