5 papers · 1 filter
A frequency-independent solver for systems of first order linear ordinary differential equations
Tony Hu, James Bremer
When a system of first order linear ordinary differential equations has eigenvalues of large magnitude, its solutions exhibit complicated behaviour, such as high-frequency oscillat…
The Levin approach to the numerical calculation of phase functions
Murdock Aubry, James Bremer
The solutions of scalar ordinary differential equations become more complex as their coefficients increase in magnitude. As a consequence, when a standard solver is applied to such…
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…