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On the numerical solution of second order ordinary differential equations in the high-frequency regime. (English) Zbl 1380.65119

Summary: We describe an algorithm for the numerical solution of second order linear ordinary differential equations in the high-frequency regime. It is based on the recent observation that solutions of equations of this type can be accurately represented using nonoscillatory phase functions. Unlike standard solvers for ordinary differential equations, the running time of our algorithm is independent of the frequency of oscillation of the solutions. We illustrate this and other properties of the method with several numerical experiments.

MSC:

65L05 Numerical methods for initial value problems involving ordinary differential equations
34A30 Linear ordinary differential equations and systems
34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
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