APPOROXIMATE SOLUTION OF LAPLACE'S EQUATION

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Anie Ekpes 2012-1-9

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https://ww2.mathworks.cn/matlabcentral/answers/25694-apporoximate-solution-of-laplace-s-equation

PLEASE I HAVE THIS QUESTION:

APPROXIMATE THE SOLUTION OF LAPLACE'S EQUATION IN THE SQUARE ABCD FOR THE BOUNDARY CONDITIONS INDICATED BELOW WITH THE SPACING h=1/6 for the following values of the parameters.
α=0.9+0.1,k; k=0,1,2; β=1.01+0.02,n; n=0,1,2;
Carry out Iterations to within 10-²
J=  1  2  3  4  5  6
u/AD  0  17.28  29.05α  40.00  29.05β  17.28
u/BC  0  9.81  17.98 α  29.12  38.25 β  42.31
u/AB  0  0  0  0  0  0
u/DC  4.31  6.98  12.38 β  19.14  30.10 α  40.16

CAN YOU PLEASE HELP ME ON A PROGRAM TO GET IT SOLVED USING GAUSS SEIDEL I NEED TO SUBMIT IT IN 3 DAYS TIME, THANKS THESE ARE THE EQUATION I USED MANUALLY:

L1=0.25*(0+L6+L2+17.28)

L2=0.25*(L1+L7+L3+29.05α

L3=0.25*(L2+L8+L4+40)

L4=0.25*(L3+L9+L5+29.05β

L5=0.25*(L4+L10+6.98+17.28)

L6=0.25*(0+L11+L7+L1)

L7=0.25*(L6+L12+L8+L12)

L8=0.25*(L7+L13+L9+L3)

L9=0.25*(L8+L14+L10+L4)

L10=0.25*(L9+L15+12.38β+L5)

L11=0.25*(0+L16+L12+L6)

L12=0.25*(L11+L17+L13+L7)

L13=0.25*(L12+L18+L14+L8)

L14=0.25*(L13+L19+L15+L9)

L15=0.25*(L14+L20+19.14+L10)

L16=0.25*(0+L21+L17+L11)

L17=0.25*(L16+L22+L18+L12)

L18=0.25*(L17+L23+L19+L13)

L19=0.25*(L18+L24+L20+L14)

L20=0.25*(L19+L25+30.10α+L15)

L21=0.25*(0+0+L22+L16)

L22=0.25*(L21+9.81+L23+L17)

L23=0.25*(L22+17.98α+L24+L18)

L24=0.25*(L23+29.12+L25+L19)

L25=0.25*(L24+38.25β+40.16+L20)

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Walter Roberson 2012-1-9

Which equation are you trying to solve? In written form, not by name.

Anie Ekpes 2012-1-10

I AM TRYING TO SOLVE THE PROBLEM USING GAUSS SEIDEL METHOD, I HAVE DONE IT MANUALLY BUT I NEED TO ITERATE IT FOR 10 TIMES AND THE MESH POINTS ARE 25, MEANING I HAVE TO SOLVE 250 EQUATIONS.

THIS IS THE EQUATION I USED MANUALLY: