I'm looking at the BVP: [tex]y'' + ay' + e^{ax}y = 1[/tex], with y(0) = 0 and y(10) = 0. The numerical solution blows up at certain values of [tex]a[/tex]. For example, a near 0.089 and a near 0.2302. Why does this happen and how do I predict it?
Erm. I found the problem. Near those values of 'a', there exists a zero eigenvalue of the linear operator. I guess that means that, [tex]y'' + ay' + e^{ax}y = 0\cdot u^* = 1[/tex], is a possible solution, and thus the eigenfunction [tex]u^* \to \infty[/tex] will cause the blowup. Is this correct? It's been a while since I've done Sturm-Liouville stuff.