Hybrid Chebyshev function bases for sparse spectral methods in parity-mixed PDEs on an infinite domain

Benjamin Miquel, Keith Julien
2017 Journal of Computational Physics  
We present a numerical spectral method to solve systems of differential equations on an infinite interval y∈ (-∞, ∞) in presence of linear differential operators of the form Q(y) (∂/∂_y)^b (where Q(y) is a rational fraction and b a positive integer). Even when these operators are not parity-preserving, we demonstrate how a mixed expansion in interleaved Chebyshev rational functions TB_n(y) and SB_n(y) preserves the sparsity of their discretization. This paves the way for fast O(N N) and
more » ... ly accurate mixed implicit-explicit time-marching of sets of linear and nonlinear equations in unbounded geometries.
doi:10.1016/j.jcp.2017.08.034 fatcat:jxvuxzx7v5anhiookvim547bqi