Homework 1

Math 8442

Numerical Analysis and Scientific Computing

Spring, 2014

Instructor: Mitchell Luskin

Due: February 24, 2014

• Problem 1
  

  Homework 13.1 in Luskin notes.

• Problem 2
  

  Homework 13.2 in Luskin notes.

• Problem 3
  

  Show that the Leapfrog or midpoint method for the wave equation is second order accurate in space and time. Show that the Leapfrog method is stable if and only if it satisfies the CFL condition.

• Problem 4
  

  Show that the trapezoidal method for the wave equation is second order accurate in space and time. Show that the trapezoidal method is unconditionally stable.