7 citations · 33 across the 26 of their papers we have counts for
28 papers
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…
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…
A framework for stable spectral methods in -dimensional unit balls
Jing Gao, Arieh Iserles
The subject of this paper is the design of efficient and stable spectral methods for time-dependent partial differential equations in unit balls. We commence by sketching the desir…
A recurrence relation for generalised connection coefficients
Jing Gao, Arieh Iserles
We formulate and prove a general recurrence relation that applies to integrals involving orthogonal polynomials and similar functions. A special case are connection coefficients be…
On skyburst polynomials and their zeros
María José Cantero, Arieh Iserles
We consider polynomials orthogonal on the unit circle with respect to the complex-valued measure , where . We derive their explic…
Orthogonal systems for time-dependent spectral methods
Arieh Iserles
This paper is concerned with orthonormal systems in real intervals, given with zero Dirichlet boundary conditions. More specifically, our interest is in systems with a skew-symmetr…