Solving a second-order boundary value equation on a non-uniform mesh
<p>I have an equation of the form </p>

<p><code>y'' + a(x) y' + b(x) y = f(x)
y(0) = y(1) = 1</code></p>

<p>where <code>x</code> is non-uniformly spaced. </p>

<p>How can I solve this type of second-order boundary value problem in python? </p>

<p>Are you searching for the family of functions [ y<sub>x</sub><code>(t)</code> ] where <code>t</code> is the variable on which you derive <code>y</code>?</p>

<p>Are your boundary conditions true for all x?</p>

<p>You might want to look at <a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.integrate.ode.html" rel="nofollow">http://docs.scipy.org/doc/scipy/reference/generated/scipy.integrate.ode.html</a></p>

python numpy scipy numerical-methods differential-equations