Numerical Partial Differential Equations 1 Homework 1
(Due: Oct. 25, 2006)
1. Problem 1
Chapter 1, page 4, Example 1.1
2. Problem 2
Chapter 1, page 8, Exercise 1.1
3. Problem 3
Chapter 2, page 37, Exercise 2.2
4. Problem 4
Chapter 2, page 37, Exercise 2.3
5. Problem 5
Use (2.10) to write a program to solve the boundary value problem using the direct solver, cg method and inverse matrix:
u00(x) = f (x) for − 1 < x < 1 (1)
u(−1) = α, u(1) = β. (2)
Solve the problem with various grid sizes and the conditions below
• f(x) = 2, α = β = 1
• f(x) = 12x2, α = β = 1
• f(x) = ex, α = e−1, β = e1 Discuss the results.
