On the numerical solution of second order differential equations in the high-frequency regime
For scientists and engineers needing efficient solutions to highly oscillatory ODEs, this algorithm removes the frequency-dependent computational cost of standard solvers.
The paper presents an algorithm for solving second-order linear differential equations in the high-frequency regime, achieving a running time independent of oscillation frequency. Numerical experiments demonstrate its effectiveness.
We describe an algorithm for the numerical solution of second order linear differential equations in the highly-oscillatory regime. It is founded on the recent observation that the 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 the performance of the method with several numerical experiments.