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Liouville-Green approximations via the Riccati transformation. (English) Zbl 0618.34011
Consider the scalar second order equation on (a,b) $u''=f(t)u$ with $f(t)=p(t)\sp 2+q(t)$ or $f(t)=-p(t)\sp 2+q(t),$ 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.
Reviewer: G.Caristi

34A45Theoretical approximation of solutions of ODE
34B05Linear boundary value problems for ODE
Full Text: DOI
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