Efficient spectral-Galerkin method II.: direct solvers of second- and fourth-order equations using Chebyshev polynomials

A Class of Sparse Spectral Operators for Inversion of Powers of the Laplacian in N Dimensions

Journal of Scientific Computing

Chebyshev finite difference approximation for the boundary value problems

Applied Mathematics and Computation

Essential imposition of Neumann condition in Galerkin-Legendre elliptic solvers

Journal of Computational Physics

Stokes eigenmodes in square domain and the stream function-vorticity correlation

Journal of Computational Physics

A Legendre spectral method in time for first-order hyperbolic equations

Applied Numerical Mathematics

A stable, high-order method for three-dimensional, bounded-obstacle, acoustic scattering

Journal of Computational Physics

An efficient direct parallel spectral-element solver for separable elliptic problems

Journal of Computational Physics

Efficient spectral-Galerkin algorithms for direct solution of fourth-order differential equations using Jacobi polynomials

Applied Numerical Mathematics

Efficient multi-dimensional solution of PDEs using Chebyshev spectral methods

Journal of Computational Physics

Spectral methods in linear stability. Applications to thermal convection with variable gravity field

Applied Numerical Mathematics

Efficient spectral ultraspherical-dual-Petrov-Galerkin algorithms for the direct solution of (2n+1)th-order linear differential equations

Mathematics and Computers in Simulation

3D phase-field simulations of interfacial dynamics in Newtonian and viscoelastic fluids

Journal of Computational Physics

Combinations of collocation and finite-element methods for Poisson's equation

Computers & Mathematics with Applications

Optimal Error Estimates of the Legendre Tau Method for Second-Order Differential Equations

Journal of Scientific Computing

Numerical solution of the Poisson equation over hypercubes using reduced Chebyshev polynomial bases

Journal of Computational and Applied Mathematics

A numerical comparison of Chebyshev methods for solving fourth order semilinear initial boundary value problems

Journal of Computational and Applied Mathematics

About the ellipticity of the Chebyshev-Gauss-Radau discrete Laplacian with Neumann condition

Journal of Computational Physics

A Legendre Petrov-Galerkin method for fourth-order differential equations

Computers & Mathematics with Applications

A spectral-Galerkin continuation method using Chebyshev polynomials for the numerical solutions of the Gross-Pitaevskii equation

Journal of Computational and Applied Mathematics

Matrix decomposition algorithms for elliptic boundary value problems: a survey

Numerical Algorithms

Spectral Chebyshev Collocation for the Poisson and Biharmonic Equations

SIAM Journal on Scientific Computing

Second kind integral equations for the first kind Dirichlet problem of the biharmonic equation in three dimensions

Journal of Computational Physics

Efficient Spectral Sparse Grid Methods and Applications to High-Dimensional Elliptic Problems

SIAM Journal on Scientific Computing

An error minimized pseudospectral penalty direct Poisson solver

Journal of Computational Physics

Jacobi spectral method with essential imposition of Neumann boundary condition

Applied Numerical Mathematics

Efficient spectral-Galerkin methods for systems of coupled second-order equations and their applications

Journal of Computational Physics

A fourth order finite difference method for the Dirichlet biharmonic problem

Numerical Algorithms

Crank-Nicolson/quasi-wavelets method for solving fourth order partial integro-differential equation with a weakly singular kernel

Journal of Computational Physics

A GPU parallelized spectral method for elliptic equations in rectangular domains

Journal of Computational Physics