[SciPy-User] scipy.integrate.solve_bvp with explicit dependence on independent variable?

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[SciPy-User] scipy.integrate.solve_bvp with explicit dependence on independent variable?

Boyan Penkov
Hello all,

I am trying to use scipy.integrate.solve_bvp to solve a boundary value
problem of a function in one variable -- $\phi(r)$ --  for a
cylindrical geometry.

The examples here are pretty good:
https://docs.scipy.org/doc/scipy-0.18.1/reference/generated/scipy.integrate.solve_bvp.html

However, when casting into a ocupled first-order system, the issue
here is that I have explicit dependence on the independent variable
$r$.

When I write the equivalent of

>>> def fun(x, y):
...     return np.vstack((y[1], -np.exp(y[0])))

, the interpreter promptly replies "TypeError: only length-1 arrays
can be converted to Python scalars" -- this makes sense, since

So, can scipy.integrate.solve_bvp be used in problems where there's an
explicit dependence on $r$, for functions where the right-hand side is
F(dq/dx, q, r)?

Cheers!

--
Boyan Penkov
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Re: scipy.integrate.solve_bvp with explicit dependence on independent variable?

Pauli Virtanen-3
ke, 2017-10-25 kello 16:01 -0400, Boyan Penkov kirjoitti:
[clip]
> So, can scipy.integrate.solve_bvp be used in problems where there's
> an
> explicit dependence on $r$, for functions where the right-hand side
> is
> F(dq/dx, q, r)?

Does "dq/dx" mean "dq/dr" and equation of type

d^2 q/dr^2 = F(dq/dr, q, r)

Then the yes, the independent variable is the first argument in
"def fun(r, y)". If this is not what you are looking for, if you write
explicitly the first order system you want to solve maybe better
answers come.

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Pauli Virtanen
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Re: scipy.integrate.solve_bvp with explicit dependence on independent variable?

Boyan Penkov

--
Boyan Penkov
www.boyanpenkov.com

On Oct 25, 2017, at 18:51, Pauli Virtanen <[hidden email]> wrote:

ke, 2017-10-25 kello 16:01 -0400, Boyan Penkov kirjoitti:
[clip]
So, can scipy.integrate.solve_bvp be used in problems where there's
an
explicit dependence on $r$, for functions where the right-hand side
is
F(dq/dx, q, r)?

Does "dq/dx" mean "dq/dr" and equation of type

d^2 q/dr^2 = F(dq/dr, q, r)

Whoops, yeah….  you are correct, I do indeed mean dq/dr...


Then the yes, the independent variable is the first argument in
"def fun(r, y)". If this is not what you are looking for, if you write
explicitly the first order system you want to solve maybe better
answers come.

The issue seems to be that I then generally have 

x = linspace(….)

which makes the output of fun(x,y) have length len(x) + 1 and not just 2, as may be expected.

Is there a syntactic solution to this?

--
Pauli Virtanen
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