0
$\begingroup$

I have BVP.

$y'' + 2y' - \frac{4}{x}y = 1$

$y'(\frac{1}{2}) = \frac{3}{2}; y(1) + y'(1) = 4$

$\frac{1}{2} \le x \le 1$

How can I solve it using shooting method? How can I get $y(a) = A $ and $y(b) = B$. And how cand I calculate $y(b,\alpha)$?

I will appreciate any help and links to theoretical material which can help.

$\endgroup$
0
$\begingroup$

As the differential equation is linear, the result depends linearly on the initial conditions. Thus solve once with $y'(\frac12)=0$ and once with $y'(\frac12)=1$ and find by linear interpolation the parameter $a$ where the second boundary condition is met for $y'(\frac12)=a$.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.