Question: Error, (in dsolve/numeric/bvp/convertsys) too many boundary conditions: expected 6, got 7

> restart;
> with(plots);
> Eq1 := diff(f(eta), eta, eta, eta)+f(eta)*(diff(f(eta), eta, eta))-2*(diff(f(eta), eta))^2-M^2*(diff(f(eta), eta)) = 0;
/ d / d / d \\\ / d / d \\
|----- |----- |----- f(eta)||| + f(eta) |----- |----- f(eta)||
\ deta \ deta \ deta /// \ deta \ deta //

2
/ d \ 2 / d \
- 2 |----- f(eta)| - M |----- f(eta)| = 0
\ deta / \ deta /
> Eq2 := 1+(4/3)*R*(diff(theta(eta), eta, eta))+Pr*(f(eta)*(diff(theta(eta), eta))-(diff(f(eta), eta))*theta(eta)) = 0;
4 / d / d \\
1 + - R |----- |----- theta(eta)||
3 \ deta \ deta //

/ / d \ / d \ \
+ Pr |f(eta) |----- theta(eta)| - |----- f(eta)| theta(eta)| = 0
\ \ deta / \ deta / /
> bcs1 := f(0) = S, (D(f))(0) = 1+L*G, (D(D(f)))(0) = .1, f(6) = 0;
f(0) = S, D(f)(0) = 1 + L G, @@(D, 2)(f)(0) = 0.1, f(6) = 0
> fixedparameter := [S = .1, M = .1];
[S = 0.1, M = 0.1]
> Eq3 := eval(Eq1, fixedparameter);
/ d / d / d \\\ / d / d \\
|----- |----- |----- f(eta)||| + f(eta) |----- |----- f(eta)||
\ deta \ deta \ deta /// \ deta \ deta //

2
/ d \ / d \
- 2 |----- f(eta)| - 0.01 |----- f(eta)| = 0
\ deta / \ deta /
> fixedparameter := [R = .1, Pr = .7];
[R = 0.1, Pr = 0.7]
> Eq4 := eval(Eq2, fixedparameter);
/ d / d \\ / d \
1 + 0.1333333333 |----- |----- theta(eta)|| + 0.7 f(eta) |----- theta(eta)|
\ deta \ deta // \ deta /

/ d \
- 0.7 |----- f(eta)| theta(eta) = 0
\ deta /
> bcs2 := theta(0) = 1+T*B, (D(theta))(6) = B, theta(6) = 0;
theta(0) = 1 + T B, D(theta)(6) = B, theta(6) = 0

> T := .1; B := .1;
0.1
0.1
> L := [0., .1, .2, .3];
[0., 0.1, 0.2, 0.3]
> for k to 4 do R := dsolve(eval({Eq3, Eq4, bcs1, bcs2}, L = L[k]), [f(eta), theta(eta)], numeric, output = listprocedure); Y || k := rhs(R[2]); YL || k := rhs(R[3]) end do;
Error, (in dsolve/numeric/bvp/convertsys) too many boundary conditions: expected 6, got 7
> plot([YL || (1 .. 4)], 0 .. 6, 1 .. -.2, labels = [eta, diff(f(eta), eta)]);

 

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