The Follow problem need to be solved! These Problems are just the reference from
ID: 2077583 • Letter: T
Question
The Follow problem need to be solved!
These Problems are just the reference from the LAST PROBLEM SET. DONT NEED TO BE SOLVED!
3.* Given the same problem as in the last problem set: a square with sides of length L 1 and potentials on the boundaries of V (0, y) V (a, 0) 100 and V (1, y) V (a, 1) 0. Solve this problem using separation of variables; (treat it as the sum of two potentials each with three sides of zero potential.) Evaluate your answer on an 11 by 11 grid matching that of the problem on the previous set so that you can compare directly the two solutions.Explanation / Answer
Relaxation method involves taking average of nearest nieghbors , each element in the grid has 7 nearest neighbors
. starting from the given assumption the iterations are
I st:
50
0 100
0 46 100
0 35 60 100
0 23 42 50 100
0 0 0 0 0 50
II nd:
50
0 100
0 42 100
0 38 56 100
0 19 38 49 100
0 0 0 0 0 50
III rd:
50
0 100
0 42 100
0 36 54 100
0 18 37 42 100
0 0 0 0 0 50
IV th:
50
0 100
0 41 100
0 35 53 100
0 18 35 41 100
0 0 0 0 0 50
Vth:
50
0 100
0 41 100
0 35 52 100
0 17 35 41 100
0 0 0 0 0 50
VI th :
50
0 100
0 41 100
0 35 52 100
0 17 35 41 100
0 0 0 0 0 50
VII th :
50
0 100
0 41 100
0 35 52 100
0 17 35 41 100
0 0 0 0 0 50
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