Question: solve two coupled equation

 

Hi

 

I want to solve the equation of

F'''(x)+F(x)*F''(x)=0

with the following  boundary conditions

F(-5)=F'(-5)=0

F'(5)=0.14

for solving it numerically in the computational domain of [-5...5]. I have seprated the domain into two parts and the governing equation and boundary condition in each domain is assumed as follows


g'''(x)+g(x)*g''(x)=0
g(0)=alpha
g(-5)=0
g'(-5)=0

and

h'''(x)+h(x)*h''(x)=0
h(0)=alpha
h'(0)=beta
h'(5)=0.14

Employing the continuty of the second or third derivative of g or h at x=0 like follow

h''(0)=g''(0)

h'''(0)=g'''(0)
, I want to find the numerical value of alpha and beta.
please help me


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