4 papers
Phase function methods for second order inhomogeneous linear ordinary differential equations
Kirill Serkh, James Bremer
It is well known that second order homogeneous linear ordinary differential equations with slowly varying coefficients admit slowly varying phase functions. This observation underl…
A quasilinear complexity algorithm for the numerical simulation of scattering from a two-dimensional radially symmetric potential
James Bremer
Standard solvers for the variable coefficient Helmholtz equation in two spatial dimensions have running times which grow quadratically with the wavenumber . Here, we describe a…
Fast Algorithms for the Multi-dimensional Jacobi Polynomial Transform
James Bremer, Qiyuan Pang, Haizhao Yang
We use the well-known observation that the solutions of Jacobi's differential equation can be represented via non-oscillatory phase and amplitude functions to develop a fast algori…
Improved estimates for nonoscillatory phase functions
James Bremer, Vladimir Rokhlin
Recently, it was observed that solutions of a large class of highly oscillatory second order linear ordinary differential equations can be approximated using nonoscillatory phase f…