The “phase function” method to solve second-order asymptotically polynomial differential equations. (English) Zbl 1256.65080

This paper uses Liouville-Green asymptotic theory to compute the zeros of the solutions, via an asymptotic numerical approximation to a phase function, and the solutions themselves of the problem \(y''+ q(x)y= 0\). Here, \(q(x)\) is asymptotically polynomial. Examples of this approach are given for various simple polynomial and rational forms of \(q(x)\).


65L99 Numerical methods for ordinary differential equations
34A05 Explicit solutions, first integrals of ordinary differential equations


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