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Question: Numerical solution of challenging ODE

Question:Numerical solution of challenging ODE

robin1234 5 Maple
ode dsolve numeric stiff bc
May 25 2016
1

Hello everybody.

I'm trying to obtain the numerical solution of a differential equation. Unfortunately, this prove to be quite challenging. I was able to obtain a rough solution using mathematica, but nothing more. The function is strictly increasing (for sure).

Any help is really REALLY appreciated, thanks!

 

``

deq1 := 1/(b-f(b)) = (2*(3-(1-f(b)*(diff(f(b), b, b)))/((diff(f(b), b))*(diff(f(b), b)))))/(1-2*(b-(1-f(b))/(diff(f(b), b))))

1/(b-f(b)) = 2*(3-(1-f(b)*(diff(diff(f(b), b), b)))/(diff(f(b), b))^2)/(1-2*b+2*(1-f(b))/(diff(f(b), b)))

 (1)

ic1 := eval(f(b), b = 3/8) = 0, eval(f(b), b = 1/2) = 1/2

f(3/8) = 0, f(1/2) = 1/2

 (2)

digits := 3

3

 (3)

dsol1 := dsolve({deq1, ic1}, method = bvp[middefer], numeric, range = 3/8 .. 1/2)

Error, (in dsolve/numeric/bvp) initial Newton iteration is not converging

  

``

 

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