12 citations · 41 across the 12 of their papers we have counts for
5 papers · 1 filter
A frame approach for equations involving the fractional Laplacian
Ioannis P. A. Papadopoulos, Timon S. Gutleb, José A. Carrillo +1
Exceptionally elegant formulae exist for the fractional Laplacian operator applied to weighted classical orthogonal polynomials. We utilize these results to construct a solver, bas…
Explicit fractional Laplacians and Riesz potentials of classical functions
Timon S. Gutleb, Ioannis P. A. Papadopoulos
We prove and collect numerous explicit and computable results for the fractional Laplacian with as well as its whole space inverse, the Riesz potential, $(-Δ)^{…
Building hierarchies of semiclassical Jacobi polynomials for spectral methods in annuli
Ioannis P. A. Papadopoulos, Timon S. Gutleb, Richard M. Slevinsky +1
We discuss computing with hierarchies of families of (potentially weighted) semiclassical Jacobi polynomials which arise in the construction of multivariate orthogonal polynomials.…
A static memory sparse spectral method for time-fractional PDEs
Timon S. Gutleb, José A. Carrillo
We introduce a method which provides accurate numerical solutions to fractional-in-time partial differential equations posed on with withou…
Polynomial and rational measure modifications of orthogonal polynomials via infinite-dimensional banded matrix factorizations
Timon S. Gutleb, Sheehan Olver, Richard Mikael Slevinsky
We describe fast algorithms for approximating the connection coefficients between a family of orthogonal polynomials and another family with a polynomially or rationally modified m…