Soal-soal:
S0262 – Analisis Numerik (Pertemuan 13)
Partial Differential Equation
Solution Technique
For this, the plate is treated as a grid of discrete points
y
0,n+1
i,j+1
i,j
i-1,j
i+1,j
x
0,0
m+1,0
i,j-1
9
TWO DIMENSIONAL LAPLACE EQUATION
Example: A 4 4 heated plate, where all sides are kept at constant
temperature as given in the following figure: How the temperature
distributed?
T= 100oC
T= 75oC
T= 50oC
T= 0oC
13
TWO DIMENSIONAL LAPLACE EQUATION
Solution:
Boundary conditions:
T= 100oC
T0,4
T4,4
T1, 0  T2, 0  T3, 0  0
T1, 4  T2, 4  T3, 4  100
T0,1  T0, 2  T0,3  75
T= 75oC
T= 50oC
T4,1  T4, 2  T4,3  4
Corner points 
T0, 0  (0  75) / 2  37.5
T0,1
T0, 4  (0  50) / 2  25
T4, 4  (100  50) / 2  75
T0,0
T1,0
T= 0oC
T4,0
T4, 0  (75  100) / 2  87.5
14
TWO DIMENSIONAL LAPLACE EQUATION
Solution:
Ti 1, j  Ti 1, j  Ti , j 1  Ti , j 1  4Ti , j  0
T= 100oC
T0,4
T= 75oC
T4,4
T= 50oC
The above
equation will be
used to solve the
temperature of
inner points
T0,1
T0,0
T1,0
T= 0oC
T4,0
15
Selesaikan soal di atas untuk menentukan temperature pada titik
yang belum diketahui: T1,1 , T2,1 , T3,1 , T1, 2 , T2, 2 , T3, 2 , T1,3 , T2,3 , dan T3,3