Hi @Faraz j
Fixing the vpasolve() syntax does return some complex-valued solutions, with their real parts close to the values of your user-supplied solutions: (
, 
) and (
, 
). Also, check if E1 = 13.7872 and E2 = 11.3728 are rounded to 6 digits of precision. If you use the true values, perhaps you can obtain the real-valued solutions.
, ) and (, ). Also, check if E1 = 13.7872 and E2 = 11.3728 are rounded to 6 digits of precision. If you use the true values, perhaps you can obtain the real-valued solutions.% ------------ Parameters --------------------
a = 0.9;
beta_10 = 3.5668;
k0 = 4.9907;
K2 = 480;
% ------------ Required Functions --------------------
syms g(x) h1(y) h2(y) v(x)
g(x) = 1.177.*sin((pi.*x)./a).^2;
h1(y) = 1-275.*(y-1).^2;
h2(y) = -14.*(y-1);
h(y) = h1(y) + 1i*h2(y);
v(x) = 1.517+1.833.*x.^2;
% ------------ Equation Functions --------------------
syms x1 x2 y1 y2
Fn1 = ((cos((beta_10/k0)*y1*v(x1))-cos(y1*v(x1)))/sin(y1*v(x1)))*(sin(pi*x1)/a);
Fn2 = ((cos((beta_10/k0)*y2*v(x2))-cos(y2*v(x2)))/sin(y2*v(x2)))*(sin(pi*x2)/a);
Ya1_G0 = (K2*Fn1^2) / (((K2*Fn1^2)/(g(x1)*h(y1)))+(3.0691-13.7872i));
Ya2_G0 = (K2*Fn2^2) / (((K2*Fn2^2)/(g(x2)*h(y2)))+(-1.9145-11.3728i));
% ------------ Equations --------------------
E1 = imag((K2*Fn1^2)/(g(x1)*h(y1))) == 13.7872;
E2 = imag((K2*Fn2^2)/(g(x2)*h(y2))) == 11.3728;
E3 = Ya2_G0/Fn2 == - 2*(Ya1_G0/Fn1);
E4 = Ya1_G0 + Ya2_G0 == 0.5;
E = [E1,E2,E3,E4];
S = vpasolve(E, [x1,x2,y1,y2], [a/4 -a/4 0.98 1.02])
