Solve first order system using bvp4c

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Day Rosli 2016-1-25

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https://ww2.mathworks.cn/matlabcentral/answers/265148-solve-first-order-system-using-bvp4c

编辑： Day Rosli 2016-1-26

Hi, I have problem to solve this in MATLAB. The equation already in first order system, yet I still confused to write the code and solve it. Or this equation cant be solved by using bvp4c perhaps?

Equation:

y(1)'=y(2);
((mu*y(2)')/R)=(((W-mu')*y(2))/R)+((i*R*(Abar*U+Bbar*V-Obar)+U)/R)*y(1)-(2*(1+V)/R)*y(5)+(Abarone*U'+Bbar*V')*y(3)+i*(kappa^2-((Abar*(i))/R))*y(4);
y(3)'=-i*y(1);
y(4)'=((i*(y(1)*W-(y(1)*mu)'))/R)-((i*R*(Abar*U+Bbar*V-Obar)+W')/R)*y(3);
y(5)'=y(6);
((mu*y(6)')/R)=(((W-mu')*y(6))/R)+((i*R*(Abar*U+Bbar*V-Obar)+U)/R)*y(5)+(2*(1+V)/R)*y(1)+(Abarone*V'-Bbar*U')*y(3)+i*(Bbar/R)*y(4);

with bc:

y(1)(0)=ya(2)(0)=ya(3)(0)=ya(4)(0)=ya(5)(0)=ya(6)(0)=0;
y(1)(infinity)=y(2)(infinity)=y(3)(infinity)=y(4)(infinity)=y(5)(infinity)=y(6)(infinity)=0;

where infinity = 20;

where;

i is imaginary number;
mu=((U'(x))^2+(V'(x))^2)^((n-1)/2);
Obar=(R^(n-1)/2)*omega;
Abarone=Abar-(i/R);
kappa=Abar^2+Bbar^2;
R=n=Abar=Bbar=1;
omega=0;

For U(x),V(x),W(x),U'(x),V'(x) and W'(x), the values I already got from previous computation. meaning each of them have values from x=0 until x=20.

The problem now is that,

1) How do I write the system in MATLAB since the mu' term makes it more confusing (for me).
2) Notice that there is U(x),V(x),W(x),U'(x),V'(x) and W'(x) which have their own values ranging from x=0 till x=20. How can I relate this 
problem from my previous computation? Do I need to paste the values in the system for each U(x),V(x),W(x),U'(x),V'(x) and W'(x)? 
Or is there other thing I can do?
3) Also, there is 12 boundary conditions where I only have 6 first order equations. Im so confused.