MATLAB: How to solve a system of linear equations (56 unknown Variables – 56 equations)

system of linear equations (56 unknown variables - 56 equations)

with regards , how to solve this system of linear equations ? (56 equations)

(unknown Variables are : b1 c1 d1 e1 g1 f1 s1 q1 b2 c2 d2 e2 g2 f2 s2 q2 b3 c3 d3 e3 g3 f3 s3 q3 b4 c4 d4 e4 g4 f4 s4 q4 b5 c5 d5 e5 g5 f5 s5 q5 b6 c6 d6 e6 g6 f6 s6 q6 b7 c7 d7 e7 g7 f7 s7 q7 )

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One way is eliminating one variable at a time; see attached.

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MATLAB: I am writing a code to solve 5 simultaneous equations with 5 unknowns. I am using the function vpasolve, however the code takes 50 minutes to run. Is there a quicker way of solving the equations

I would do this numerically, using fsolve. It requires a slight re-write of your equations to make them all implicit.

Example —

syms Qa_1 Q1_1 Q2_1 Q3_1 Q4_1 real
eqn1 = (Qa_1 - (Q1_1 + Q2_1 + Q3_1 + Q4_1));
eqn2 = (Qa_1^2/60.51 + Q1_1^2/0.8616 - (1.035/Q1_1 + 24.3/Qa_1));
eqn3 = (Qa_1^2/60.51 + Q2_1^2/1.346 - (1.321/Q2_1 + 16.57/Qa_1));
eqn4 = (Qa_1^2/60.51 + Q3_1^2/1.346 - (1.236/Q3_1 + 8.873/Qa_1));
eqn5 = (Qa_1^2/60.51 + Q4_1^2/1.346 - (1.044/Q4_1 + 1.619/Qa_1));
Eqnsfcn = matlabFunction([eqn1, eqn2, eqn3, eqn4, eqn5], 'Vars',{[Qa_1, Q1_1, Q2_1, Q3_1, Q4_1]});
B0 = rand(1,5)*100;
[B,fval] = fsolve(Eqnsfcn, B0)

This was almost instantaneous. There are likely multiple roots, so experiment with different initial parameter estimates (here ‘B0’).

EDIT — This version makes it easier to track the individual variable names:

Eqnsfcn = matlabFunction([eqn1, eqn2, eqn3, eqn4, eqn5], 'Vars',{Qa_1, Q1_1, Q2_1, Q3_1, Q4_1});
B0 = rand(1,5)*100;
[B,fval] = fsolve(@(b)Eqnsfcn(b(1),b(2),b(3),b(4),b(5)), B0)

MATLAB: How to solve a set of 32 non-linear equations using symbolic solver

If you try to proceed by solving the first 11 equations for the first 11 variables in your list, you will fail, because the 11th variable in your list does not appear in the first 11 equations. The 11th equation involves some of the first 10 variables, together with V_d2, which is the 16th variable in your list. You would need to solve the first 16 equations for the first 16 variables for that to work out.

The inherent limit on the number of equations that can be solved simultaneously is very big -- large enough that it is certain that you would run out of memory before you hit the limit.

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MATLAB: I am writing a code to solve 5 simultaneous equations with 5 unknowns. I am using the function vpasolve, however the code takes 50 minutes to run. Is there a quicker way of solving the equations

MATLAB: How to solve a set of 32 non-linear equations using symbolic solver

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