A fast algorithm for particle simulations
Journal of Computational Physics
A fast algorithm for the numerical evaluation of conformal mappings
SIAM Journal on Scientific and Statistical Computing
Rapid solution of integral equations of scattering theory in two dimensions
Journal of Computational Physics
A modified Chebyshev pseudospectral method with an O(N–1) time step restriction
Journal of Computational Physics
A fast direct algorithm for the solution of the Laplace equation on regions with fractal boundaries
Journal of Computational Physics
Roundoff error in computing derivatives using the Chebyshev differentiation matrix
Journal of Computational Physics
Implicit-explicit methods for time-dependent partial differential equations
SIAM Journal on Numerical Analysis
Boundary Layer Resolving Pseudospectral Methods for Singular Perturbation Problems
SIAM Journal on Scientific Computing
Accuracy Enhancement for Higher Derivatives using Chebyshev Collocation and a Mapping Technique
SIAM Journal on Scientific Computing
Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations
Applied Numerical Mathematics - Special issue on time integration
A new class of time discretization schemes for the solution of nonlinear PDEs
Journal of Computational Physics
Journal of Computational Physics
Fast spectral projection algorithms for density-matrix computations
Journal of Computational Physics
SIAM Journal on Matrix Analysis and Applications
Hi-index | 31.45 |
We present a method for the numerical solution of partial differential equations using spectral collocation. By employing a structured representation of linear operators we are able to use fast algorithms without being restricted to periodic boundary conditions. The underlying ideas are introduced and developed in the context of linearly implicit methods for stiff equations. We show how different boundary conditions may be applied and illustrate the technique on the Allen-Cahn equation and the diffusion equation.