I am trying to solve this equation in MMA 11.3
$2 \epsilon s^{\prime \prime}+\frac{1-s}{2 \epsilon}=0$;
BCs: $s^{\prime}( \pm 1)=0$ and $s\left(0\right)=0$;
The analytical solution is expressed as:$s^{ \pm}(x)=1-\cosh \left(\frac{x}{2 \epsilon}\right) \pm \operatorname{coth}\left(\frac{1}{2 \epsilon}\right) \sinh \left(\frac{x}{2 \epsilon}\right)$.
However, the solution from MMA 11.3 test code is not corret:
Code
pf = DSolve[{s''[x]*2*\[Epsilon] + 0.5 (1 - s[x])/\[Epsilon] == 0,
s[0] == 0, s'[-1] == 0, s'[1] == 0}, s, x]
if we validate the solution:
\[Epsilon] = 0.009
Plot[Evaluate[s[x] /. pf], {x, -1, 1}]
now how can we derive the correct solution in MMA?
{}
as the output withDSolve::bvnul
warning, have youClear[s]
? 2. You should solve withs[0] == 0, s'[-1] == 0
ands[0] == 0, s'[1] == 0
separately. $\endgroup$