MA 512
Homework 2
February 10, 2005
1. (10 points) Using MATLAB or the language/environment of your choice, apply the
classical 4th-order Runge-Kutta method to the initial-value problem of Homework 1,
problem 1:
y = y + et cos t,
y(0) = 0
over the interva
MA 512
Homework 1
February 3, 2005
1. (10 points) Using Matlab or the language/environment of your choice, apply the
rst-order forward Euler method to the initial-value problem
y = y + et cos t,
y(0) = 0
over the interval [0, ]. (The exact solution is y(t
MA 512
Homework 3
February 17, 2005
The object of this assignment is to familiarize you further with MATLABs ODE
solving capabilities (and rkf45 in particular), to acquaint you with several interesting
autonomous ODEs, and to demonstrate the usefulness of
MA 512
Homework 5
March 10, 2005
It is noted in the text (problem 42, page 457) that the method
yn+1 = yn +
h2
h
yn + yn+1 +
y yn+1
2
12 n
(1)
is a fourth-order method for which the region of absolute stability contains the entire
negative real axis. In (
MA 512
Homework 4
February 24, 2005
1. (10 points) The illustration below shows the boundaries of the absolute-stability
regions for RungeKutta methods of orders 1, 2, and 4. (The 4th-order method is the
classical one.) Using the method or approach of you
MA 512
Homework 6
March 17, 2005
The object of this assignment is to familiarize you with the usage and functioning of
a simple second-order predictor-corrector method and also to introduce you to a new
and fascinating ODE (problem 1). The method is imple
MA 512
Homework 7
March 31, 2005
The object of this assignment is to familiarize you with the usage and functioning of
MATLABs ode15s and to heighten your appreciation for sti ODE solvers. You will
also become acquainted with another interesting ODE.
1. (
MA 512
Final Exam
April 21, 2005
This is a take-home nal due on or before Monday, May 2. In working it, you may
consult any books or notes. You may not get help or discuss it with anyone except
me.
1. (15 points) The object of this problem is to demonstra
MA 512
Homework 8
April 7, 2005
The objects of this assignment are, in problem 1, to demonstrate the comparative
performance of the Jacobi, GaussSeidel, and SOR methods on our model Poisson
problem and, in problem 2, to further illustrate the role of the