Q3. Use the finite-difference approach with the one iteration of Gauss-Seidel method to solve the following equation d?T + 0.01(20 – T) = o dx2 with the boundary conditions T(0) = 40 and T(10) = 200 and the step size, Ax = 2. Employ the three- point central difference approximation for the second derivative and compare your result with the true analytical solution at x = 6. Analytical solution of the equation above is T = 73.4523e0.1x – 53.4523e-0.1x + 20

Advanced Engineering Mathematics
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Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Q3. Use the finite-difference approach with the one iteration of Gauss-Seidel method to solve the
following equation
d?T
+ 0.01(20 – T) = 0
dx2
with the boundary conditions T(0) = 40 and T(10) = 200 and the step size, Ax = 2. Employ the three-
point central difference approximation for the second derivative and compare your result with the
true analytical solution at x = 6.
Analytical solution of the equation above is T = 73.4523e0.1x – 53.4523e¬0.1x + 20
Transcribed Image Text:Q3. Use the finite-difference approach with the one iteration of Gauss-Seidel method to solve the following equation d?T + 0.01(20 – T) = 0 dx2 with the boundary conditions T(0) = 40 and T(10) = 200 and the step size, Ax = 2. Employ the three- point central difference approximation for the second derivative and compare your result with the true analytical solution at x = 6. Analytical solution of the equation above is T = 73.4523e0.1x – 53.4523e¬0.1x + 20
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