PHYS 535 - Computational Methods in Physics
Assignment 1 (60 points total)
Due Monday, Jan. 18, 2009 at noon
1. (20 points) Using any analytical technique you wish, derive the 5-point dierence equations for
the rst and second derivatives of a function, fo
Section 7.7
Deriving the Trapezoidal Rule Error
The error bounds for numerical integration are presented without proof. While it is
perhaps unreasonable to prove all of them in an introductory text, one should at least
prove the bound for the Trapezoidal
S EC . 9.6
505
P REDICTOR -C ORRECTOR M ETHODS
Adams-Bashforth-Moulton Method
9.6 Predictor-Corrector Methods
The methods of Euler, Heun, Taylor, and Runge-Kutta are called single-step methods
because they use only the information from one previous point