Liouville-Green approximations via the Riccati transformation (Q1089145)

Consider the scalar second order equation on (a,b) \(u''=f(t)u\) with \(f(t)=p(t)^ 2+q(t)\) or \(f(t)=-p(t)^ 2+q(t),\) being p positive and piecewise differentiable and q piecewise continuous. Under suitable conditions on f, using a Riccati transformation, fundamental solutions are found and these are used to provide Liouville-Green approximations and explicit error bounds.