Hello,
I am attempting to solve a system of nonlinear equations, but unfortunately, vpasolve couldn't find any solutions.
Here is my code:
syms g(x) h1(y) h2(y) v(x)
g(x) = 1.177.*sin((pi.*x)./a).^2;
v(x) = 1.517+1.833.*x.^2;
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));
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;
S = vpasolve(E,[x1,x2,y1,y2],[-a/4 a/4;-a/4 a/4;0.98 1.02;0.98 1.02])
Before asking, YES, there are solutions. The desired answers are (x1 = 0.086, y1 = 1.0125) and (x2 = -0.176, y2 = 1.0099), or anything close to that, like (x1 = 0.085, y1 = 1.0126) and (x2 = -0.175, y2 = 1.0097).
How can I find a solution? I appreciate your assistance in advance.