Now showing items 1-13 of 13

• Article

#### Finite Difference Schemes for the Cauchy–Navier Equations of Elasticity with Variable Coefficients ﻿

(2015)
We solve the variable coefficient Cauchy–Navier equations of elasticity in the unit square, for Dirichlet and Dirichlet-Neumann boundary conditions, using second order finite difference schemes. The resulting linear systems ...
• Article

#### Legendre Gauss spectral collocation for the Helmholtz equation on a rectangle ﻿

(2004)
A spectral collocation method with collocation at the Legendre Gauss points is discussed for solving the Helmholtz equation -Δu+κ(x,y)u=f(x,y) on a rectangle with the solution u subject to inhomogeneous Robin boundary ...
• Article

#### A legendre spectral collocation method for the biharmonic Dirichlet problem ﻿

(2000)
A Legendre spectral collocation method is presented for the solution of the biharmonic Dirichlet problem on a square. The solution and its Laplacian are approximated using the set of basis functions suggested by Shen, which ...
• Article

#### A Legendre spectral Galerkin method for the biharmonic Dirichlet problem ﻿

(2001)
A Legendre spectral Galerkin method is presented for the solution of the biharmonic Dirichlet problem on a square. The solution and its Laplacian are approximated using the set of basis functions suggested by Shen, which ...
• Article

#### A Legendre spectral quadrature Galerkin method for the Cauchy-Navier equations of elasticity with variable coefficients ﻿

(2017)
We solve the Dirichlet and mixed Dirichlet-Neumann boundary value problems for the variable coefficient Cauchy-Navier equations of elasticity in a square using a Legendre spectral Galerkin method. The resulting linear ...
• Article

#### Matrix decomposition algorithms for elliptic boundary value problems: A survey ﻿

(2011)
We provide an overview of matrix decomposition algorithms (MDAs) for the solution of systems of linear equations arising when various discretization techniques are applied in the numerical solution of certain separable ...
• Article

#### Matrix decomposition algorithms for modified spline collocation for Helmholtz problems ﻿

(2003)
We consider the solution of various boundary value problems for the Helmholtz equation in the unit square using a nodal cubic spline collocation method and modifications of it which produce optimal (fourth-) order ...
• Article

#### Modified nodal cubic spline collocation for three-dimensional variable coefficient second order partial differential equations ﻿

(2013)
We formulate a fourth order modified nodal cubic spline collocation scheme for variable coefficient second order partial differential equations in the unit cube subject to nonzero Dirichlet boundary conditions. The approximate ...
• Article

#### A nonoverlapping domain decomposition method for Legendre spectral collocation problems ﻿

(2007)
We consider the Dirichlet boundary value problem for Poisson's equation in an L-shaped region or a rectangle with a cross-point. In both cases, we approximate the Dirichlet problem using Legendre spectral collocation, that ...
• Article

#### Optimal superconvergent one step nodal cubic spline collocation methods ﻿

(2006)
We formulate new optimal (fourth) order one step nodal cubic spline collocation methods for the solution of various elliptic boundary value problems in the unit square. These methods are constructed so that the respective ...
• Article

#### Optimal superconvergent one step quadratic spline collocation methods ﻿

(2008)
We formulate new optimal quadratic spline collocation methods for the solution of various elliptic boundary value problems in the unit square. These methods are constructed so that the collocation equations can be solved ...
• Article

#### Spectral Chebyshev collocation for the poisson and biharmonic equations ﻿

(2010)
This paper is concerned with the spectral Chebyshev collocation solution of the Dirichlet problems for the Poisson and biharmonic equations in a square. The collocation schemes are solved at a cost of 2N3 + O(N2 logN) ...
• Article

#### Spectral Chebyshev-Fourier collocation for the Helmholtz and variable coefficient equations in a disk ﻿

(2008)
The paper is concerned with the spectral collocation solution of the Helmholtz equation in a disk in the polar coordinates r and θ. We use spectral Chebyshev collocation in r, spectral Fourier collocation in θ, and a simple ...