# Sparse spectral-tau method for the three-dimensional helically reduced wave equation on two-center domains

@article{Lau2011SparseSM, title={Sparse spectral-tau method for the three-dimensional helically reduced wave equation on two-center domains}, author={Stephen R. Lau and Richard H. Price}, journal={J. Comput. Phys.}, year={2011}, volume={231}, pages={7695-7714} }

## 17 Citations

### A New Legendre Collocation Method for Solving a Two-Dimensional Fractional Diffusion Equation

- Mathematics
- 2014

A new spectral shifted Legendre Gauss-Lobatto collocation (SL-GL-C) method is developed and analyzed to solve a class of two-dimensional initial-boundary fractional diffusion equations with variable…

### The next subsection describes the helically reduced Navier Stokes equations

- Computer Science
- 2014

A partial motivation for this work has been the ongoing development of similar spectral methods for the construction binary neutron star spacetimes.

### Stellar surface as low-rank modification in iterative methods for binary neutron stars

- Computer Science, PhysicsJ. Comput. Phys.
- 2017

### Sparse Spectral-Element Methods for the Helically Reduced Einstein Equations

- PhysicsLecture Notes in Computational Science and Engineering
- 2020

We describe ongoing work towards construction—via multidomain, modal, spectral methods—of helically symmetric spacetimes representing binary neutron stars. Adopting “particle” models, we focus here…

### A space-time collocation scheme for modified anomalous subdiffusion and nonlinear superdiffusion equations

- Mathematics
- 2016

Abstract.This paper reports a new spectral collocation technique for solving time-space modified anomalous subdiffusion equation with a nonlinear source term subject to Dirichlet and Neumann boundary…

### A spectral technique for solving two-dimensional fractional integral equations with weakly singular kernel

- Mathematics
- 2017

This paper adapts a new numerical technique for solving two- dimensional fractional integral equations with weakly singular. Using the spectral collocation method, the fractional operators of…

### A NEW SPECTRAL ALGORITHM FOR TIME-SPACE FRACTIONAL PARTIAL DIFFERENTIAL EQUATIONS WITH SUBDIFFUSION AND SUPERDIFFUSION

- Mathematics
- 2016

This paper reports a new spectral collocation algorithm for solving time-space fractional partial differential equations with subdiffusion and superdiffusion. In this scheme we employ the shifted…

### A review of operational matrices and spectral techniques for fractional calculus

- Mathematics
- 2015

Recently, operational matrices were adapted for solving several kinds of fractional differential equations (FDEs). The use of numerical techniques in conjunction with operational matrices of some…

### A review of operational matrices and spectral techniques for fractional calculus

- MathematicsNonlinear Dynamics
- 2015

Recently, operational matrices were adapted for solving several kinds of fractional differential equations (FDEs). The use of numerical techniques in conjunction with operational matrices of some…

## References

SHOWING 1-10 OF 48 REFERENCES

### Multidomain spectral method for the helically reduced wave equation

- MathematicsJ. Comput. Phys.
- 2007

### Periodic standing-wave approximation: Nonlinear scalar fields, adapted coordinates, and the eigenspectral method

- Mathematics
- 2005

The periodic standing wave (PSW) method for the binary inspiral of black holes and neutron stars computes exact numerical solutions for periodic standing-wave spacetimes and then extracts approximate…

### Periodic standing-wave approximation: Post-Minkowski computations

- Physics
- 2007

The periodic standing-wave method studies circular orbits of compact objects coupled to helically symmetric standing-wave gravitational fields. From this solution an approximation is extracted for…

### Integration Preconditioning of Pseudospectral Operators. I. Basic Linear Operators

- Mathematics
- 1998

This paper develops a family of preconditioners for pseudospectral approximations of pth-order linear differential operators subject to various types of boundary conditions. The approximations are…

### Initial data for black hole evolutions

- Physics
- 2003

We discuss the initial value problem of general relativity in its recently unified Lagrangian and Hamiltonian pictures and present a multi-domain pseudo-spectral collocation method to solve the…

### Periodic standing-wave approximation: Computations in full general relativity

- Physics
- 2009

The periodic standing-wave method studies circular orbits of compact objects coupled to helically symmetric standing-wave gravitational fields. From this solution an approximation is extracted for…

### Preconditioning Chebyshev Spectral Collocation by Finite-Difference Operators

- Mathematics
- 1997

In 1979 Orszag proposed a finite-difference preconditioning of the Chebyshev collocation discretization of the Poisson equation. In 1984 Haldenwang, Labrosse, Abboudi, and DeVille gave analytic…

### An efficient spectral method for ordinary differential equations with rational function coefficients

- MathematicsMath. Comput.
- 1996

The authors present some relations that allow the efficient approximate inversion of linear differential operators with rational function coefficients, including all the classical orthogonal polynomials, in terms of a large class of orthogomatic polynomial families.