Holistic Numerical Methods

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MULTIPLE CHOICE TEST

(All Tests)

SHOOTING METHOD

(More on Shooting Method)

ORDINARY DIFFERENTIAL EQUATIONS

(More on Ordinary Differential Equations)

 

Pick the most appropriate answer.


The exact solution to the boundary value problem

, ,  

for  is

-234.66

0.0000

16.000

106.66


Given

, , , the exact value of  is

 

-72.0

0.00

 36.0

72.0


Given

, , ,

If one was using shooting method with Eulerís method with a step size of, and an assumed value of =20, then the estimated value of y(12) in the first iteration most nearly is

160.0

496.0

1088

1102


The transverse deflection, u of a cable of length, L, fixed at both ends, is given as a solution to

where

 

T = tension in cable

R = flexural stiffness

q = distributed transverse load

Given are, , , .  The shooting method is used with Eulerís method assuming a step size of.  Initial slope guesses at x=0 of  and  are used in order, and then refined for the next iteration using linear interpolation after the value of u(L) is found.  The deflection in inches at the center of the cable found during the second iteration is most nearly

 

0.03583

0.08083

0.08484

0.08863


The radial displacement, u is a pressurized hollow thick cylinder (inner radius=5″, outer radius=8″) is given at different radial locations.

Radius

Radial Displacement

(in)

(in)

5.0

0.0038731

5.6

0.0036165

6.2

0.0034222

6.8

0.0032743

7.4

0.0031618

8.0

0.0030769

 

The maximum normal stress, in psi, on the cylinder is given by

The maximum stress, in psi, with second order accuracy is

2079.3

2104.5

2130.7

2182.0

Hint:, and

 

           

where

           

 


For a simply supported ( at  and ) beam with a uniform load q, the deflection v(x) is described by the boundary value ordinary differential equation as

            ,

where

            E = Youngís modulus of elasticity of beam

            I = second moment of cross-sectional area.

This is based on assuming that  is small; if  is not small, then the ordinary differential equation is

 


Complete Solution

Multiple choice questions on other topics


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Copyrights: University of South Florida, 4202 E Fowler Ave, Tampa, FL 33620-5350. 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# Creative Commons License0126793, 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 Attribution-NonCommercial-NoDerivs 3.0 Unported License.

 

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