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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 \(q(x)\).

MSC:

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

Software:

Mathematica
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References:

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