MATLAB: How to solve linear and non linear equation system

matrices algebranonlinear

Hello

Can anyone tell me how I can solve the following system of equation

1) a1v1-a2v2-a3v3-a4v4=0

2) a3v3-a5v5-a6v6=0

3) a2v2+a6v6-a7v7=0

4) a7v7+a5v5+a4v4-a8v8=0

5) 500v1^2+p1-p2-500v2^2=0

6) 500v1^2+p1-p3-500v3^2=0

7) 500v1^2+p1-p4-500v4^2=0

8) 500v3^2+p3-p5-500v5^2=0

9) 500v3^2+p3-p6-500v6^2=0

10) 500v7^2+p7-p2-500v2^2=0

11) 500v7^2+p7-p6-500v6^2=0

12) 500v8^2+p8-p4-500v4^2=0

13) 500v8^2+p8-p5-500v5^2=0

14) 500v8^2+p8-p7-500v7^2=0

How to solve the above equation system for v's and p's where v1 and p1 are known

Please guide!!!

Regards

Best Answer

For 14 equations with 14 unknowns, try fsolve, or any other iterative solver (Newton-Raphson, Arc-Length, line search, etc...) Make a function which takes 14-element vectors, and gives as output the left-hand sides of the 14 equations. Then you will try to make this function equal to zero.

Related Solutions

MATLAB: Does fsolve seem not iterate towards the solution

k = 0.1007;
rZ = 12.6518;
Rs = 0.164;
Cmax = 7.0e-11;
W = 1.704e8;
iZ = 14.5273;
Ls = 1.1e-7;
a1 = (k/1000)^2*(rZ-Rs);
a2 = (Cmax/100*W)^2*(rZ-Rs);
a3 = -k/1000;
b1 = k^2*(iZ-W*Ls);
b2 = k^2*W*Ls/200;
b3 = W*Ls/200*(Cmax*W)^2;
b4 = (Cmax*W)^2*(iZ-W*Ls);
A = (a2*b1-b2*a3+a1*b4)/(a1*b1);
B = (-a3*b3+a2*b4)/(a1*b1);
disk = A^2/4-B;
if disk >=0
  x21squared = -A/2+sqrt(disk);
  x22squared = -A/2-sqrt(disk);
end
solx1 = zeros(4,1);
solx2 = zeros(4,1);
iflag1 = 0;
if x21squared >= 0
  iflag1 = 1;
  solx2(1) = sqrt(x21squared);
  solx2(2) = -sqrt(x21squared);
end
iflag2 = 0;
if x22squared >= 0
  iflag2 = 1;
  solx2(3) = sqrt(x22squared);
  solx2(4) = -sqrt(x22squared);
end
solx1 = zeros(4,1);
if iflag1 == 1
  solx1(1) = -a3/(a1*solx2(1)^2+a2);
  solx1(2) = -a3/(a1*solx2(2)^2+a2);
end
if iflag2 == 1
  solx1(3) = -a3/(a1*solx2(3)^2+a2);
  solx1(4) = -a3/(a1*solx2(4)^2+a2);
end
if iflag1 == 1
  solx1(1)
  solx2(1)
  solx1(2)
  solx2(2)
  a1*solx1(1)*solx2(1)^2+a2*solx1(1)+a3
  b1*solx2(1)^2+b2*solx1(1)*solx2(1)^2+b3*solx1(1)+b4
  a1*solx1(2)*solx2(2)^2+a2*solx1(2)+a3
  b1*solx2(2)^2+b2*solx1(2)*solx2(2)^2+b3*solx1(2)+b4
end
if iflag2 == 1
  solx1(3)
  solx2(3)
  solx1(4)
  solx2(4)
  a1*solx1(3)*solx2(3)^2+a2*solx1(3)+a3
  b1*solx2(3)^2+b2*solx1(3)*solx2(3)^2+b3*solx1(3)+b4
  a1*solx1(4)*solx2(4)^2+a2*solx1(4)+a3
  b1*solx2(4)^2+b2*solx1(4)*solx2(4)^2+b3*solx1(4)+b4  
end

MATLAB: Need help to form equations

a = rand(1,4); % your a matrix
syms v1 v2 v3 v4
S = solve( a(1)*v1^2-a(2)*v2-a(3)*v3^2-a(4)*v4==0,...
 a(3)*v3^2-a(4)*v4-a(1)*v1==0,...
 a(1)*v1+a(4)*v4-a(3)*v3^2==0,...
 a(2)*v2+a(1)*v1+a(3)*v3-a(4)*v4==0)
S = 
      v1: [4x1 sym]
      v2: [4x1 sym]
      v3: [4x1 sym]
      v4: [4x1 sym]

To display the solutions, access the elements of the structure array S

S.v1
ans =
                                                                             0
                                            0.76082746713182598996024745838092
   - 0.38041373356591299498012372919046 - 0.65889591443313132581875790778993*i
   - 0.38041373356591299498012372919046 + 0.65889591443313132581875790778993*i

Best Answer

Related Solutions

MATLAB: Does fsolve seem not iterate towards the solution

MATLAB: Need help to form equations

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