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 Euler’s 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 Euler’s 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.
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 = Young’s modulus of elasticity of beam I = second moment of crosssectional area.
This is based on assuming that is small; if is not small, then the ordinary differential equation is

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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. 
