Question

4. Solve the heat equation ut = 0.2uxx on a digital computer using a. Simple explicit method b. Barakat and Clark ADE method TABLE 1 Number of Case Grid Points r 1 11 0.25 2 11 0.5 3 16 0.5 4 11 1.00 5 11 2.00 for the initial condition u(x,0) = 100sin(?x/L) L=1 and boundary conditions u(0,t) = u(L,t) = 0 Compute to t= 0.5 using the parameters in Table 1 (if possible) and compare graphically with the exact solution. c. using the Crank-Nicolson scheme.

          4. Solve the heat equation ut = 0.2uxx on a digital computer using
a. Simple explicit method
b. Barakat and Clark ADE method

TABLE 1
Number of
Case Grid Points r
1 11 0.25
2 11 0.5
3 16 0.5
4 11 1.00
5 11 2.00

for the initial condition
u(x,0) = 100sin(?x/L) L=1

and boundary conditions
u(0,t) = u(L,t) = 0

Compute to t= 0.5 using the parameters in Table 1 (if possible) and compare graphically with the exact solution.

c. using the Crank-Nicolson scheme.

4. Solve the heat equation ut = 0.2uxx on a digital computer using
a. Simple explicit method
b. Barakat and Clark ADE method

TABLE 1
Number of
Case Grid Points r
1 11 0.25
2 11 0.5
3 16 0.5
4 11 1.00
5 11 2.00

for the initial condition
u(x,0) = 100sin(?x/L) L=1

and boundary conditions
u(0,t) = u(L,t) = 0

Compute to t= 0.5 using the parameters in Table 1 (if possible) and compare graphically with the exact solution.

c. using the Crank-Nicolson scheme.

Added by Heather C.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Shyam P

Step 1

The heat equation is given by: $$ \frac{\partial u}{\partial t} = \alpha \frac{\partial^2 u}{\partial x^2} $$ Show more…

Show all steps

Thanks for your feedback!

Solve the heat equation ut = 0.2uxx on a digital computer using a. Simple explicit method b. Barakat and Clark ADE method TABLE 1 Number of Case Grid Points r 1 11 0.25 2 11 0.5 3 16 0.5 4 11 1.00 5 11 2.00 for the initial condition u(x,0) = 100sin(πx/L) L=1 and boundary conditions u(0,t) = u(L,t) = 0 Compute to t= 0.5 using the parameters in Table 1 (if possible) and compare graphically with the exact solution. c. using the Crank-Nicolson scheme.