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math.NA2024
Spectral methods on a triangle and W-systems
Jing Gao, Arieh Iserles
We present an overarching framework for stable spectral methods on a triangle, defined by a multivariate W-system and based on orthogonal polynomials on the triangle. Motivated by…
math.NA2024
Mathematical foundations of spectral methods for time-dependent PDEs
Arieh Iserles
The contention of this paper is that a spectral method for time-dependent PDEs is basically no more than a choice of an orthonormal basis of the underlying Hilbert space. This choi…