# Question:Solution to BVP , pls help

## Question:Solution to BVP , pls help

Maple

Am trying to valid a research work done by kuiken(1968)

Kuiken_(1968).pdf

where we have this two eauations:

restart;
Digits := 35;
with(ODETools);
with(student);
with(plots);
inf := 4;
equ1 := diff(f[0](eta), `\$`(eta, 3))+theta[0](eta);
equ2 := diff(theta[0](eta), `\$`(eta, 2))+3*f[0](eta)*(diff(theta[0](eta), eta));
Bcs1 := f[0](0) = 0, (D(f[0]))(0) = 0, theta[0](0) = 1, theta[0](inf) = 0, (D(D(f[0])))(inf) = 0;
S1 := dsolve({Bcs1, equ1, equ2}, {f[0](eta), theta[0](eta)}, type = numeric, method = bvp[midrich]);
proc(x_bvp)  ...  end;
S1(0);
[                            d
[eta = 0., f[0](eta) = 0., ----- f[0](eta) = 0.,
[                           deta

d   /  d            \
----- |----- f[0](eta)| = 0.82449782146165697398999365896678734,
deta \ deta          /

theta[0](eta) = 1.0000000000000000000000000000000000,

d                                                         ]
----- theta[0](eta) = -0.71098574970825563256340736114251047]
deta                                                       ]
S1(inf);
[
[eta = 4., f[0](eta) = 1.7815670728545914261072119522795076,
[

d
----- f[0](eta) = 0.51061876174095320088291844433043562,
deta

d   /  d            \
----- |----- f[0](eta)| = 0., theta[0](eta) = 0.,
deta \ deta          /

d
----- theta[0](eta) = -0.000054818176138173095945902421930470836
deta

]
]
]

Pls, I need to find the function of the limit of f[0](eta) at eta tend to infinity. checked equation 45 of the attached document and for the two equation pls checked equation 36 and 37 for the ODE equation solved above.

Kuiken_solution for equation 36 and 37.pdf

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