AMATH 342, Winter 2015: Assignment 4 (Computational)
Instructor: Hans De Sterck
Oce: MC 6108
e-mail: [email protected]
Due Date: Friday March 6, beginning of class
1. (20 marks) You are asked to
AMATH 342, Winter 2015: Assignment 6 (Computational)
Instructor: Hans De Sterck
Oce: MC 6108
e-mail: [email protected]
Due Date: Monday April 6, beginning of class
1. (20 marks) Sti ODE problem.
AMATH 342, Winter 2015: Assignment 5 (Theoretical)
Instructor: Hans De Sterck
Oce: MC 6108
e-mail: [email protected]
Due Date: Thursday March 19, beginning of class
1. (10 marks) Consider the TR
AMATH 342, Winter 2015: Assignment 3 (Theoretical)
Instructor: Hans De Sterck
Oce: MC 6108
e-mail: [email protected]
Due Date: Friday February 6, beginning of class
Note: throughout this assignme
AMATH 342, Winter 2015: Assignment 2 (Computational)
Instructor: Hans De Sterck
Oce: MC 6108
e-mail: [email protected]
Due Date: Friday January 30, beginning of class
1. (5 marks) Download the le
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 T
AMATH 342, Winter 2015: Theoretical Assignment 1
Instructor: Hans De Sterck
Oce: MC 6108
e-mail: [email protected]
Due Date: Thursday January 22, beginning of class
1. (5 marks) Show that the loc
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
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 no
AMATH 342, Winter 2015: formula sheet version 1.0
I Introduction
Taylor: u(t0 + h) = u(t0 ) + u (t0 ) h + u (t0 )/(2!) h2 + O(h3 )
Taylor:
n
f (t) =
f (k) (t0 )
f (n+1) (t)
(t t0 )k +
(t t0 )n+1
k!