Question

Give the steps in solving the Residue and Relaxation method.

Answer 1

Residue method 1) If zza is a simple of F(2) then [Res F(2) 2:a = lim (2-a) f(2) 2) If aza is a pole of onder on of f/2) then kes f/2) = lim td fa-aind [ (2-a) f(2) za Res 1/2Jz-a - 2an-danil Reladation Method Consider a set of ear is axta y faz 2 = di with la,l> faltas bidtbay + bez zde bil> 1 b2l+ 1631 GX + egy +32 zdz 1917 191+ K31 Now, define residuals R = d - ax - azy - Azz R2 - do-bp-bzy - b32 اور لاع -وف سی Draw operating table a IR - a relaxation table R | Rg 61-a 2 ba T-az bz 1-3 (If there is no change in variable 24,2) 8x - sy = S2 =0 then residuals are Ri=d, R = de Rg=ds If Sxal, then residual (R) && decreased by (d-ai) Hence -a, 8x=1 4 saa _d Here -ve and the eign means increasing a decorearing the values 2

Therefore if variable se os increaung then recidual is decoracing as you can see in above residuals ear that increasing in de will increasing in R,} Therefore, in relaxation method we change the value of - 4y 2 to convert residuals as a zerore Now; choose the numerically larger residual say "de If we chang "sx" by " then decidual "R" will be decreased by rde

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