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On well-conditioned spectral collocation and spectral methods by the integral reformulation
Kui Du
Well-conditioned spectral collocation and spectral methods have recently been proposed to solve differential equations. In this paper, we revisit the well-conditioned spectral coll…
Preconditioning rectangular spectral collocation
Kui Du
Rectangular spectral collocation (RSC) methods have recently been proposed to solve linear and nonlinear differential equations with general boundary conditions and/or other constr…
Preconditioning fractional spectral collocation
Kui Du
Fractional spectral collocation (FSC) method based on fractional Lagrange interpolation has recently been proposed to solve fractional differential equations. Numerical experiments…
Two spectral methods for 2D quasi-periodic scattering problems
Kui Du
We consider the 2D quasi-periodic scattering problem in optics, which has been modelled by a boundary value problem governed by Helmholtz equation with transparent boundary conditi…