On symmetrizing the ultraspherical spectral method for self-adjoint problems
For researchers in numerical analysis and spectral methods, this provides a more efficient and stable approach to solving self-adjoint problems.
The paper presents a symmetrization mechanism for the ultraspherical spectral method, yielding symmetric and banded discretizations, and an adaptive spectral decomposition algorithm for self-adjoint operators. Applications demonstrate the method's properties.
A mechanism is described to symmetrize the ultraspherical spectral method for self-adjoint problems. The resulting discretizations are symmetric and banded. An algorithm is presented for an adaptive spectral decomposition of self-adjoint operators. Several applications are explored to demonstrate the properties of the symmetrizer and the adaptive spectral decomposition.