Solve the system of equations
GIVEN
A system of three equations
FIND
(a) The solution of the system of equation using Jacobi and Gauss-Seidel iteration
Since we do not know the physical problem these equations originated from, it is difficult to make a
good first guess. Let’s use 0 for all three temperatures as an initial guess.
If we solve the equations in the order given for T1, T2, and T3 and solve by iteration, we find that the
solution is not stable. Let’s solve the first equation for T1, the second for T3, and the third for T2. For
Jacobi iteration we have
and for Gauss-Seidel iteration we have
The solution was carried out using a spreadsheet as shown on the next page
Applying the criterion that the temperature change per iteration should be less than 0.001, we see that
Jacobi iteration requires 7 iterations while Gauss-Seidel iteration requires 6 iterations.
You might also like to view...
Which of the following expresses the major idea of Hubble's Law?
A) There must have been a Big Bang. B) All galaxies are moving away from us equally fast. C) The more distant a galaxy is from us, the faster it moves away from us. D) The closer a galaxy is to us, the faster it moves away from us. E) More distant galaxies appear younger.
A Doppler effect occurs when a source of sound moves
A) towards you. B) away from you. C) either of these D) neither of these
Which of the following best sums up current scientific thinking about the nature of dark energy?
A) Dark energy most likely consists of a form of photons that we can't see or detect. B) Dark energy is most likely made up of weakly interacting particles that do not interact with light. C) Dark energy probably exists, but we have little (if any) idea what it is. D) Dark energy is the source of the mind weapon used by Sith Lords in Star Wars.
The Fahrenheit scale has a ______________ degree size than the Celsius scale
Fill in the blank(s) with correct word