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 MULTIPLE CHOICE TEST PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS 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

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