AMATH 342, Winter 2015: Assignment 4 (Computational)
Instructor: Hans De Sterck
Oce: MC 6108
e-mail: hdesterck@uwaterloo.ca
Due Date: Friday March 6, beginning of class
1. (20 marks) You are asked to implement in matlab four methods for the numerical solu
AMATH 342, Winter 2015: Assignment 6 (Computational)
Instructor: Hans De Sterck
Oce: MC 6108
e-mail: hdesterck@uwaterloo.ca
Due Date: Monday April 6, beginning of class
1. (20 marks) Sti ODE problem.
Consider the nonlinear IVP
u = u2 u3
u(0) =
t [0, 2/].
AMATH 342, Winter 2015: Assignment 5 (Theoretical)
Instructor: Hans De Sterck
Oce: MC 6108
e-mail: hdesterck@uwaterloo.ca
Due Date: Thursday March 19, beginning of class
1. (10 marks) Consider the TR method. Give the rst and the second characteristic poly
AMATH 342, Winter 2015: Assignment 3 (Theoretical)
Instructor: Hans De Sterck
Oce: MC 6108
e-mail: hdesterck@uwaterloo.ca
Due Date: Friday February 6, beginning of class
Note: throughout this assignment, you can use Matlab or Maple wherever it is helpful,
AMATH 342, Winter 2015: Assignment 2 (Computational)
Instructor: Hans De Sterck
Oce: MC 6108
e-mail: hdesterck@uwaterloo.ca
Due Date: Friday January 30, beginning of class
1. (5 marks) Download the les question1Driver.m and BackwardEuler.m from the class
AMATH 342
Winter 2015: Assignment 1 Solutions
Total Marks: 35
1. (5 marks) Show that the local truncation error Tn+1 of the MP rule is O(t3 ). (Hint:
Assume that vn = un and vn1 = un1 , and work out Tn+1 = un+1 vn+1 using Taylor series.
Alternatively, you
AMATH 342, Winter 2015: Theoretical Assignment 1
Instructor: Hans De Sterck
Oce: MC 6108
e-mail: hdesterck@uwaterloo.ca
Due Date: Thursday January 22, beginning of class
1. (5 marks) Show that the local truncation error Tn+1 of the MP rule is O(t3 ). (Hin
Derive the 1-step BDF method.
Solution:
Choose k = 1:
Q (tn+1 ) = f (vn+1 , tn+1 ),
v
where Qv (t) interpolates vi for i = n, n + 1. WLOG take n = 0 (t0 = 0, t1 = h) and use the
Lagrange polynomial to interpolate:
Qv (t) = v0
t
ht
+ v1 .
h
h
Then, dierent
COMPUTATIONAL METHODS
FOR
DIFFERENTIAL EQUATIONS
Course Notes (partial) for
AMATH 342
Winter 2015
Prof. Hans De Sterck
Department of Applied Mathematics
University of Waterloo
January 4, 2015
These notes have been funded by
Design and typesetting by S. Ki