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MULTIPLE CHOICE TEST

(All Tests)

PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS

(More on Parabolic 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 parabolic if

B2-4AC<0

B2-4AC>0

B2-4AC=0

B2-4AC≠0

Q2. The region in which the following equation

            acts as an parabolic equation is

for all values of  x


Q3. The partial differential equation of the temperature in a long thin rod is given by

                       

If  α = 0.8 cm2/s, the initial temperature of rod is 40°C, and the rod is divided into three equal segments, the temperature at node 1 (using ∆t=0.1s) by using an explicit solution at t=0.2 sec  is

40.7134°C

40.6882°C
 40.7033°C

40.6956°C

Q4.  The partial differential equation of the temperature in a long thin rod is given by

                         

                

      If  α = 0.8 cm2/s, the initial temperature of rod is 40°C, and the rod is divided into three equal segments, the temperature at node 1 (using ∆t=0.1s) by using an implicit solution for t=0.2 sec is

  40.7134°C

  40.6882°C

  40.7033°C

   40.6956°C

Q5.  The partial differential equation of the temperature in a long thin rod is given by

            

                       

 If  α = 0.8 cm2/s, the initial temperature of rod is 40°C, and the rod is divided into three equal segments, the temperature at node 1 (using ∆t=0.1s) by using an Crank-Nicolson solution for t=0.2 sec is

40.7134°C

40.6882°C

40.7033°C

  40.6956°C

Q6.  The partial differential equation of the temperature in a long thin rod is given by

            

             

         If  α = 0.8 cm2/s, the initial temperature of rod is 40°C, and the rod is divided into three equal segments, the temperature at node 1 (using ∆t=0.1s) by using an explicit solution at  t=0.2 s is

(For node 0, ), where k=9W/(m°C), h=20W/m2, Ta=25°C and T0=(the temperature at node 0)

41.6478°C

38.435°C

39.9983°C

  37.5798°C

Complete Solution

 

 

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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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