Solving lengthy nonlinear complex equations in complex variables
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Hello Everyone!
I am trying to solve a set of 4 complex nonlinear equations in 4 complex variables, containing lengthy algebraic expressions with large complex numbers. I have tried vpasolve, solve, fsolve but all get stuck due to voluminous computations involved & no result is appeared. The expressions/equations cannot be shortened or moulded. Please provide suggestions to solve this problem. The code is as under:
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>> syms Y1s Y3s Y4s Y7s
>> e1=(220000/(sqrt(3)))/(((1.8e17*(Y3s*(4.4e63 - 2.0e63i) + Y4s*(6.9e63 - 3.1e63i) + Y7s*(9.4e63 - 4.2e63i) + Y3s*Y4s*(7.8e61 + 1.4e62i) + Y3s*Y7s*(1.1e62 + 1.9e62i) + Y4s*Y7s*(1.6e62 + 2.9e62i) - Y3s*Y4s*Y7s*(5.5e60 - 3.9e60i) - 7.0e64 - 2.1e65i))/(- Y1s*(1.2e82 + 3.7e82i) - Y3s*(1.4e82 + 4.1e82i) - Y4s*(1.5e82 + 4.3e82i) - Y7s*(2.0e82 + 5.5e82i) + Y1s*Y3s*(7.7e80 - 3.4e80i) + Y1s*Y4s*(1.2e81 - 5.4e80i) + Y3s*Y4s*(1.4e81 - 6.2e80i) + Y1s*Y7s*(1.7e81 - 7.4e80i) + Y3s*Y7s*(1.9e81 - 8.6e80i) + Y4s*Y7s*(2.0e81 - 9.2e80i) + Y1s*Y3s*Y4s*(1.4e79 + 2.4e79i) + Y1s*Y3s*Y7s*(1.9e79 + 3.3e79i) + Y1s*Y4s*Y7s*(2.9e79 + 5.1e79i) + Y3s*Y4s*Y7s*(3.4e79 + 5.9e79i) - Y1s*Y3s*Y4s*Y7s*(9.7e77 - 6.9e77i) - 9.7e83 + 2.7e83i))*484)-((3.9046-44.6295*i)*1000);
>> e3=(220000/(sqrt(3)))/(((4.4e16*(Y1s*(1.7e64 - 7.8e63i) + Y4s*(3.2e64 - 1.4e64i) + Y7s*(4.3e64 - 2.0e64i) + Y1s*Y4s*(3.1e62 + 5.4e62i) + Y1s*Y7s*(4.3e62 + 7.5e62i) + Y4s*Y7s*(7.7e62 + 1.3e63i) - Y1s*Y4s*Y7s*(2.2e61 - 1.6e61i) - 3.2e65 - 9.3e65i))/(- Y1s*(1.2e82 + 3.7e82i) - Y3s*(1.4e82 + 4.1e82i) - Y4s*(1.5e82 + 4.3e82i) - Y7s*(2.0e82 + 5.5e82i) + Y1s*Y3s*(7.7e80 - 3.4e80i) + Y1s*Y4s*(1.2e81 - 5.4e80i) + Y3s*Y4s*(1.4e81 - 6.2e80i) + Y1s*Y7s*(1.7e81 - 7.4e80i) + Y3s*Y7s*(1.9e81 - 8.6e80i) + Y4s*Y7s*(2.0e81 - 9.2e80i) + Y1s*Y3s*Y4s*(1.4e79 + 2.4e79i) + Y1s*Y3s*Y7s*(1.9e79 + 3.3e79i) + Y1s*Y4s*Y7s*(2.9e79 + 5.1e79i) + Y3s*Y4s*Y7s*(3.4e79 + 5.9e79i) - Y1s*Y3s*Y4s*Y7s*(9.7e77 - 6.9e77i) - 9.7e83 + 2.7e83i))*484)-((3.4339-39.25*i)*1000);
>> e4=(220000/(sqrt(3)))/(((5.0e3*(Y1s*(1.2e77 + 5.5e75i) + Y3s*(1.4e77 + 5.7e75i) + Y7s*(2.0e77 + 7.0e75i) + Y1s*Y3s*(1.4e74 + 2.5e75i) + Y1s*Y7s*(2.9e74 + 5.2e75i) + Y3s*Y7s*(3.7e74 + 6.1e75i) - Y1s*Y3s*Y7s*(1.1e74 - 1.7e73i) + 5.3e77 - 4.0e78i))/(Y1s*(2.4e81 - 1.7e82i) + Y3s*(2.6e81 - 1.9e82i) + Y4s*(2.7e81 - 2.0e82i) + Y7s*(3.1e81 - 2.6e82i) + Y1s*Y3s*(3.8e80 + 1.6e79i) + Y1s*Y4s*(5.9e80 + 2.8e79i) + Y3s*Y4s*(6.8e80 + 2.8e79i) + Y1s*Y7s*(8.1e80 + 3.4e79i) + Y3s*Y7s*(9.3e80 + 3.4e79i) + Y4s*Y7s*(9.9e80 + 3.5e79i) + Y1s*Y3s*Y4s*(6.9e77 + 1.2e79i) + Y1s*Y3s*Y7s*(1.0e78 + 1.7e79i) + Y1s*Y4s*Y7s*(1.5e78 + 2.6e79i) + Y3s*Y4s*Y7s*(1.8e78 + 3.0e79i) - Y1s*Y3s*Y4s*Y7s*(5.3e77 - 8.5e76i) - 4.4e83 - 8.5e82i))*484)-((1.5165-17.3338*i)*1000);
>> e7=(220000/(sqrt(3)))/(((1.2e4*(Y1s*(1.9e77 + 7.3e76i) + Y3s*(2.2e77 + 8.2e76i) + Y4s*(2.3e77 + 8.7e76i) - Y1s*Y3s*(1.1e75 - 4.2e75i) - Y1s*Y4s*(1.7e75 - 6.4e75i) - Y3s*Y4s*(2.0e75 - 7.4e75i) - Y1s*Y3s*Y4s*(1.3e74 + 2.2e73i) + 2.8e78 - 6.0e78i))/(Y1s*(2.5e82 - 4.9e82i) + Y3s*(2.7e82 - 5.5e82i) + Y4s*(2.8e82 - 5.8e82i) + Y7s*(3.5e82 - 7.5e82i) + Y1s*Y3s*(1.1e81 + 4.2e80i) + Y1s*Y4s*(1.7e81 + 6.7e80i) + Y3s*Y4s*(2.0e81 + 7.7e80i) + Y1s*Y7s*(2.4e81 + 9.2e80i) + Y3s*Y7s*(2.7e81 + 1.0e81i) + Y4s*Y7s*(2.9e81 + 1.1e81i) - Y1s*Y3s*Y4s*(1.0e79 - 3.8e79i) - Y1s*Y3s*Y7s*(1.4e79 - 5.2e79i) - Y1s*Y4s*Y7s*(2.2e79 - 8.0e79i) - Y3s*Y4s*Y7s*(2.5e79 - 9.3e79i) - Y1s*Y3s*Y4s*Y7s*(1.7e78 + 2.7e77i) - 1.2e84 - 7.0e83i))*484)-((4.8371-55.2888*i)*1000);
>> result = solve(e1,e3,e4,e7,Y1s,Y3s,Y4s,Y7s)
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Answers (2)
Alex Sha
on 29 Oct 2020
Try to find numerical solutions as below;
y1s.realpart: 11.0169967890388
y1s.imagpart: -125.141575853451
y3s.realpart: 7.81970377305325
y3s.imagpart: -106.356946529629
y4s.realpart: 3.07796056296378
y4s.imagpart: -36.8035908733627
y7s.realpart: 15.4211136064375
y7s.imagpart: -178.419654796614
2 Comments
Alex Sha
on 30 Oct 2020
Hi, ubtc, the results are obtained by 1stOpt, a math software other than Matlab, much easy for using, and without requiring the guess of initial-start valus for each parameter, the total code like below:
ComplexPar Y1s,Y3s,Y4s,Y7s;
ComplexStr = i;
Function
(220000/(sqrt(3)))/(((1.8e17*(Y3s*(4.4e63 - 2.0e63*i) + Y4s*(6.9e63 - 3.1e63*i) + Y7s*(9.4e63 - 4.2e63*i) + Y3s*Y4s*(7.8e61 + 1.4e62*i) + Y3s*Y7s*(1.1e62 + 1.9e62*i) + Y4s*Y7s*(1.6e62 + 2.9e62*i) - Y3s*Y4s*Y7s*(5.5e60 - 3.9e60*i) - 7.0e64 - 2.1e65*i))/(- Y1s*(1.2e82 + 3.7e82*i) - Y3s*(1.4e82 + 4.1e82*i) - Y4s*(1.5e82 + 4.3e82*i) - Y7s*(2.0e82 + 5.5e82*i) + Y1s*Y3s*(7.7e80 - 3.4e80*i) + Y1s*Y4s*(1.2e81 - 5.4e80*i) + Y3s*Y4s*(1.4e81 - 6.2e80*i) + Y1s*Y7s*(1.7e81 - 7.4e80*i) + Y3s*Y7s*(1.9e81 - 8.6e80*i) + Y4s*Y7s*(2.0e81 - 9.2e80*i) + Y1s*Y3s*Y4s*(1.4e79 + 2.4e79*i) + Y1s*Y3s*Y7s*(1.9e79 + 3.3e79*i) + Y1s*Y4s*Y7s*(2.9e79 + 5.1e79*i) + Y3s*Y4s*Y7s*(3.4e79 + 5.9e79*i) - Y1s*Y3s*Y4s*Y7s*(9.7e77 - 6.9e77*i) - 9.7e83 + 2.7e83*i))*484)-((3.9046-44.6295*i)*1000);
(220000/(sqrt(3)))/(((4.4e16*(Y1s*(1.7e64 - 7.8e63*i) + Y4s*(3.2e64 - 1.4e64*i) + Y7s*(4.3e64 - 2.0e64*i) + Y1s*Y4s*(3.1e62 + 5.4e62*i) + Y1s*Y7s*(4.3e62 + 7.5e62*i) + Y4s*Y7s*(7.7e62 + 1.3e63*i) - Y1s*Y4s*Y7s*(2.2e61 - 1.6e61*i) - 3.2e65 - 9.3e65*i))/(- Y1s*(1.2e82 + 3.7e82*i) - Y3s*(1.4e82 + 4.1e82*i) - Y4s*(1.5e82 + 4.3e82*i) - Y7s*(2.0e82 + 5.5e82*i) + Y1s*Y3s*(7.7e80 - 3.4e80*i) + Y1s*Y4s*(1.2e81 - 5.4e80*i) + Y3s*Y4s*(1.4e81 - 6.2e80*i) + Y1s*Y7s*(1.7e81 - 7.4e80*i) + Y3s*Y7s*(1.9e81 - 8.6e80*i) + Y4s*Y7s*(2.0e81 - 9.2e80*i) + Y1s*Y3s*Y4s*(1.4e79 + 2.4e79*i) + Y1s*Y3s*Y7s*(1.9e79 + 3.3e79*i) + Y1s*Y4s*Y7s*(2.9e79 + 5.1e79*i) + Y3s*Y4s*Y7s*(3.4e79 + 5.9e79*i) - Y1s*Y3s*Y4s*Y7s*(9.7e77 - 6.9e77*i) - 9.7e83 + 2.7e83*i))*484)-((3.4339-39.25*i)*1000);
(220000/(sqrt(3)))/(((5.0e3*(Y1s*(1.2e77 + 5.5e75*i) + Y3s*(1.4e77 + 5.7e75*i) + Y7s*(2.0e77 + 7.0e75*i) + Y1s*Y3s*(1.4e74 + 2.5e75*i) + Y1s*Y7s*(2.9e74 + 5.2e75*i) + Y3s*Y7s*(3.7e74 + 6.1e75*i) - Y1s*Y3s*Y7s*(1.1e74 - 1.7e73*i) + 5.3e77 - 4.0e78*i))/(Y1s*(2.4e81 - 1.7e82*i) + Y3s*(2.6e81 - 1.9e82*i) + Y4s*(2.7e81 - 2.0e82*i) + Y7s*(3.1e81 - 2.6e82*i) + Y1s*Y3s*(3.8e80 + 1.6e79*i) + Y1s*Y4s*(5.9e80 + 2.8e79*i) + Y3s*Y4s*(6.8e80 + 2.8e79*i) + Y1s*Y7s*(8.1e80 + 3.4e79*i) + Y3s*Y7s*(9.3e80 + 3.4e79*i) + Y4s*Y7s*(9.9e80 + 3.5e79*i) + Y1s*Y3s*Y4s*(6.9e77 + 1.2e79*i) + Y1s*Y3s*Y7s*(1.0e78 + 1.7e79*i) + Y1s*Y4s*Y7s*(1.5e78 + 2.6e79*i) + Y3s*Y4s*Y7s*(1.8e78 + 3.0e79*i) - Y1s*Y3s*Y4s*Y7s*(5.3e77 - 8.5e76*i) - 4.4e83 - 8.5e82*i))*484)-((1.5165-17.3338*i)*1000);
(220000/(sqrt(3)))/(((1.2e4*(Y1s*(1.9e77 + 7.3e76*i) + Y3s*(2.2e77 + 8.2e76*i) + Y4s*(2.3e77 + 8.7e76*i) - Y1s*Y3s*(1.1e75 - 4.2e75*i) - Y1s*Y4s*(1.7e75 - 6.4e75*i) - Y3s*Y4s*(2.0e75 - 7.4e75*i) - Y1s*Y3s*Y4s*(1.3e74 + 2.2e73*i) + 2.8e78 - 6.0e78*i))/(Y1s*(2.5e82 - 4.9e82*i) + Y3s*(2.7e82 - 5.5e82*i) + Y4s*(2.8e82 - 5.8e82*i) + Y7s*(3.5e82 - 7.5e82*i) + Y1s*Y3s*(1.1e81 + 4.2e80*i) + Y1s*Y4s*(1.7e81 + 6.7e80*i) + Y3s*Y4s*(2.0e81 + 7.7e80*i) + Y1s*Y7s*(2.4e81 + 9.2e80*i) + Y3s*Y7s*(2.7e81 + 1.0e81*i) + Y4s*Y7s*(2.9e81 + 1.1e81*i) - Y1s*Y3s*Y4s*(1.0e79 - 3.8e79*i) - Y1s*Y3s*Y7s*(1.4e79 - 5.2e79*i) - Y1s*Y4s*Y7s*(2.2e79 - 8.0e79*i) - Y3s*Y4s*Y7s*(2.5e79 - 9.3e79*i) - Y1s*Y3s*Y4s*Y7s*(1.7e78 + 2.7e77*i) - 1.2e84 - 7.0e83*i))*484)-((4.8371-55.2888*i)*1000);
The outcome will be:
y1s.realpart: 11.0169967890388
y1s.imagpart: -125.141575853451
y3s.realpart: 7.81970377305327
y3s.imagpart: -106.356946529629
y4s.realpart: 3.07796056296379
y4s.imagpart: -36.8035908733627
y7s.realpart: 15.4211136064375
y7s.imagpart: -178.419654796614
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