CSCE 340/840 Numerical Analysis I

Exam 2 Study Guide

Exam is April 12, 2001

You will have 75 minutes to earn 100 points.

The exam is closed book. You may use two 8.5” by 11” crib sheet. I would suggest that you use the one from the last exam plus a new one that you create for this exam.

Show your work for an opportunity to get partial credit. You will be graded not only on the correctness of your answer, but also on the clarity with which you express it. Be neat!

The room is crowded so please keep your eyes on your paper and not on your neighbors.

Topics

The topics for Exam 1 included covered material through Section 4.2. The topics for Exam 2 include Section 4.3 through Chapter 5. Questions on Exam 2 may require that you have knowledge of material through Section 4.2.

Numrical Integration

Trapezoid rule

Simpson rule

See Exercise Set 4.3, Problems 1-4

Construct integration rule like Exercise Set 4.3, Problems 11-14 and Exercise Set 4.7, Problem 5

Composite numerical integration

Size of h or n for a given accuracy

See Exercise Set 4.4, Problems 7-10

Romberg integration

Complete Romberg table

See Exercise Set 4.5, Problems 5-9

Adaptive Quadrature

Gaussian Quadrature

Change of variable to integrate from –1 to +1

Use of formulas, see Exercise Set 4.7, Problems 1-4

Multiple Integrals

See Exercise Set 4.8, Problems 1-4

Improper Integrals

Change of variable

See Exercise Set 4.9, Problems 1-4

Ordinary Differential Equations

Properly posed and Lipschitz constant

See Exercise Set 5.1, Problems 1-2

Euler’s Method

See Exercise Set 5.2, Problems 1-4

Higher-Order Taylor Methods

See Exercise Set 5.3, Problems 1-4

Runge-Kutta Methods

Midpoint, modified Euler, Heun’s, fourth order methods

Exercise Set 5.4, Problems 1-4

Error Control and Runge-Kutta-Fehlberg Method

Understand concept of how error control is done and derived

Multistep Methods

Know how they are derived.

Know what implicit and explicit mean

Adams Bashforth and Adams Moulton

See Exercise Set 5.6, Problems 1-5

How to get starting values

Varialble Step-Size Multistep Methods

Understand how error control is done and derived

Implications of changing the step size

Higher Order Equations and Systems of Equations

Be able to rewrite as system of first order differential equations

Like your computer assignment

See Exercise Set 5.9, Problems 2 and 6

Stability

What is absolute stability?

Error propagation

Implicit Euler Method

Be able to take a step

See Exercise Set 5.11, Problems 8 and 9

Errors in solving ordinary differential equations

Rounding error

Local turncation error

Global error

Relation to stability