(due: May 21 in class)
Problem 1 (50%):
Consider the initial value problem
dy/dt = 0.5*t*cos(y)*sin(3*y)
0 <= t <= 4.17
y(0) =5
Estimate a restriction on the timestep you can use applying a Runge Kutta scheme of order 4, such that the solution
exhibits qualitatively the correct behavior.
The region of absolute stability for a fourth order Runge Kutta scheme is (-2.78,0).
Problem 2 (0%):
This is a reading assignment: Review Norms of Vectors and Matrices. I.e., read section 7.1. In particular, review:
Def. 7.1, Def. 7.2, Def. 7.4, Def. 7.5, Def. 7.8 and
Theorems 7.6, 7.7, 7.9, 7.11
Problem 3 (50%):
Do problem 2(a) of Section 7.1 in the textbook.
No numerics part this week.
It is strongly recommended that you use this week to get done as much as possible of the numerics project.
There will be additional numerics assignments in the next few homeworks!