Chapter 1 Exercises
From: Finite Dierence Methods for Ordinary and Partial Dierential Equations
by R. J. LeVeque, SIAM, 2007. http:/www.amath.washington.edu/rjl/fdmbook
Exercise 1.1 (derivation of nite dierence formula)
Determine the interpolating polynom
Chapter 2 Exercises
From: Finite Dierence Methods for Ordinary and Partial Dierential Equations
by R. J. LeVeque, SIAM, 2007. http:/www.amath.washington.edu/rjl/fdmbook
Exercise 2.5 (accuracy on nonuniform grids)
In Example 1.4 a 3-point approximation to
Chapter 2 Exercises
From: Finite Dierence Methods for Ordinary and Partial Dierential Equations
by R. J. LeVeque, SIAM, 2007. http:/www.amath.washington.edu/rjl/fdmbook
Exercise 2.1 (inverse matrix and Greens functions)
(a) Write out the 5 5 matrix A from
Chapter 3 Exercises
From: Finite Dierence Methods for Ordinary and Partial Dierential Equations
by R. J. LeVeque, SIAM, 2007. http:/www.amath.washington.edu/rjl/fdmbook
Exercise 3.1 (code for Poisson problem)
The matlab script poisson.m solves the Poisson
Math 7663 Homework 5
1. Prove that for a square matrix A, (A) = inf A , where the inmum
is taken over all matrix norms induced by some vector norm.
2. Program the Jacobi, Gauss-Seidel, and Richardson method (all three with
relaxation parameter ) for the 5
Homework 8 due April 25: Program the leapfrog method, Lax-Friedrichs method,
Lax-Wendro method, and the upwind method (to be covered Monday) for the equation
ut + aux = 0 with a = 2 on the interval (1, 1) with periodic boundary conditions, and
0 t 0.9. Ch
Chapter 6 and 7 Exercises
From: Finite Dierence Methods for Ordinary and Partial Dierential Equations
by R. J. LeVeque, SIAM, 2007. http:/www.amath.washington.edu/rjl/fdmbook
Exercise 6.2 (Improved convergence proof for one-step methods)
The proof of conv
Chapter 5 Exercises
From: Finite Dierence Methods for Ordinary and Partial Dierential Equations
by R. J. LeVeque, SIAM, 2007. http:/www.amath.washington.edu/rjl/fdmbook
Exercise 5.8 (Use of ode113 and ode45)
Consider the third order initial value problem