Solve Equations 2x+5y=21,x+2y=8 using Gauss Jacobi method
Solution:
Total Equations are `2`
`2x+5y=21`
`x+2y=8`
From the above equations
`x_(k+1)=1/2(21-5y_(k))`
`y_(k+1)=1/2(8-x_(k))`
Initial gauss `(x,y) = (0,0)`
Solution steps are
`1^(st)` Approximation
`x_1=1/2[21-5(0)]=1/2[21]=10.5`
`y_1=1/2[8-(0)]=1/2[8]=4`
`2^(nd)` Approximation
`x_2=1/2[21-5(4)]=1/2[1]=0.5`
`y_2=1/2[8-(10.5)]=1/2[-2.5]=-1.25`
`3^(rd)` Approximation
`x_3=1/2[21-5(-1.25)]=1/2[27.25]=13.625`
`y_3=1/2[8-(0.5)]=1/2[7.5]=3.75`
`4^(th)` Approximation
`x_4=1/2[21-5(3.75)]=1/2[2.25]=1.125`
`y_4=1/2[8-(13.625)]=1/2[-5.625]=-2.8125`
`5^(th)` Approximation
`x_5=1/2[21-5(-2.8125)]=1/2[35.0625]=17.5312`
`y_5=1/2[8-(1.125)]=1/2[6.875]=3.4375`
`6^(th)` Approximation
`x_6=1/2[21-5(3.4375)]=1/2[3.8125]=1.9062`
`y_6=1/2[8-(17.5312)]=1/2[-9.5312]=-4.7656`
`7^(th)` Approximation
`x_7=1/2[21-5(-4.7656)]=1/2[44.8281]=22.4141`
`y_7=1/2[8-(1.9062)]=1/2[6.0938]=3.0469`
Equations are Divergent...
Intertions are tabulated as below
| Iteration | x | y |
| 1 | 10.5 | 4 |
| 2 | 0.5 | -1.25 |
| 3 | 13.625 | 3.75 |
| 4 | 1.125 | -2.8125 |
| 5 | 17.5312 | 3.4375 |
| 6 | 1.9062 | -4.7656 |
| 7 | 22.4141 | 3.0469 |
This material is intended as a summary. Use your textbook for detail explanation.
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