MULTIPLE CHOICE TEST 
FINITE DIFFERENCE METHOD 
ORDINARY DIFFERENTIAL EQUATIONS 
Pick the most appropriate answer. 
Q1. The exact solution to the boundary value problem , and for y(4) is 234.67 0.0000 16.000 37.333 Q2. Given , , , the value of at y(4) using the finite difference method and a step size of h=4 can be approximated by
Q3. Given , , , The value of y(4) using the finite difference method with a second order accurate central divided difference method and a step size of h=4 is 0.000 37.333 234.67 256.00 Q4. The transverse deflection u of a cable of length, L, that is fixed at both ends, is given as a solution to
where T = tension in cable R = flexural stiffness q = distributed transverse load Given L=50", T=200 lbs, q=75lbs/in, R=75x10^{6} lbsin^{2}, using finite difference method modeling with second order central divided difference accuracy and a step size of h=12.5", the value of the deflection at the center of the cable most nearly is 0.072737" 0.08832" 0.081380" 0.084843" Q5. The radial displacement, u of a pressurized hollow thick cylinder (inner radius=5″, outer radius=8″) is given at different radial locations.
The maximum normal stress, in psi, on the cylinder is given by
The maximum stress, in psi, with second order accuracy is Hint: , and
where
2079.3 2104.5 2130.7 2182.0 Q6. For a simply supported beam (at x=0 and x=L) with a uniform load q, the vertical deflection v(x) is described by the boundary value ordinary differential equation as
,
where E = Young’s modulus of elasticity of beam I = second moment of area. This ordinary differential equation is based on assuming that dv/dx is small. If dv/dx is not small, then the ordinary differential equation is given by

AUDIENCE  AWARDS  PEOPLE  TRACKS  DISSEMINATION  PUBLICATIONS 

Copyrights: University of South Florida, 4202 E Fowler Ave, Tampa, FL 336205350. All Rights Reserved. Questions, suggestions or comments, contact kaw@eng.usf.edu This material is based upon work supported by the National Science Foundation under Grant# 0126793, 0341468, 0717624, 0836981, 0836916, 0836805, 1322586. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation. Other sponsors include Maple, MathCAD, USF, FAMU and MSOE. Based on a work at http://mathforcollege.com/nm. Holistic Numerical Methods licensed under a Creative Commons AttributionNonCommercialNoDerivs 3.0 Unported License. 
