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MULTIPLE CHOICE TEST

(All Tests)

ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS

(More on Elliptic Partial Differential Equations)

PARTIAL DIFFERENTIAL EQUATIONS

(More on Partial Differential Equations)

 

Pick the most appropriate answer.


Q1.  In a general second order linear partial differential equation with two independent variables,

where A , B , C are functions of  x and y, and  D  is a function of x , y , , , then the PDE is elliptic if

B2-4AC<0

B2-4AC>0

B2-4AC=0

B2-4AC0


Q2.  The region in which the following equation

            acts as an elliptic equation is

for all values of  x


Q3. The finite difference approximation of  in the elliptic equation

            at (x,y)  can be approximated as


Q4.  Find the temperature at the interior node given in the following figure using the direct method

                       

45.19 C

48.64 C

50.00 C

56.79 C


Q5 Find the temperature at the interior node given in the following figure

                      

Using the Lieberman method and relaxation factor of 1.2, the temperature at  x-=3, y=6  estimated after 2 iterations is (use the temperature of interior nodes as 50C  for the initial guess)

52.36 C

53.57 C

56.20 C

58.64 C


Q6. Find the steady-state temperature at the interior node as given in the following figure

           

           

53.57 C

66.40 C

68.20 C

69.59 C


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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