## 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

Mathematica
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### References:

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