I have a set of 2 algebraic equations coupled with a nonlinear differential equation? How can i solve it with Finite difference method?

if true
 % The boundary conditions are B=n=1,u=0 when zeta goes to infinty
 % Solution for B, n, and u are required
 % M=1.15, alpha=.1, beta=.01
syms n(zeta) B(zeta) u(zeta) zeta
syms alpha beta M 
Eq(1)=u==M*(1-1/n);
Eq(2)=M^2*(1-1/n)+1/2*(B^2-1)+beta*(n^3-1)==0;
Eq(3)=diff(1/n*diff(B,zeta),zeta)-alpha/M*diff(B,zeta)-B+n==0
end

[Torsten]

Since n and u can be easily calculated from B, B is the only variable that needs to be solved for. Use ODE45 to do so.

Best wishes

Torsten.

[shahab ullah khan]

Thank you for your comment @ Torsten, but please guide me in regards that ODE45 can be used for boundary value problems?

[Torsten]

Why boundary value problems ?

As far as I can see, you have an initial value problem with initial condition at zeta = infinity.

But you are correct: one further condition seems to be missing since the equation for B is a second-order ODE.

Best wishes

Torsten.