Articles

Link

Analytical Upstream Collocation Solution of a Quadratically Forced Steady-State Convection-Diffusion Equation (with Eric Smith), International Journal of Numerical Methods for Heat & Fluid Flow (2012)

Purpose – The purpose of this paper is to present the analytical solution to the...

 

Link

Optimal Hermite Collocation Applied to a One-Dimensional Convection-Diffusion Equation Using an Adaptive Hybrid Optimization Algorithm (with Karen L. Ricciardi), International Journal of Numerical Methods for Heat and Fluid Flow (2009)

Purpose – The Hermite collocation method of discretization can be used to determine highly accurate...

 

Optimal Collocation Solution of the One-Dimensional Steady-State Convection-Diffusion Equation with Variable Coefficients, International Journal of Computational and Numerical Analysis and Applications (2004)

We study the Hermite collocation solution of the one-dimensional-steady-state convection-diffusion equation with Dirichlet boundary conditions....

 

Analytical Upstream Collocation Solution of a Forced Steady-State Convection-Diffusion Equation, International Journal of Differential Equations and Applications (2003)

We give herein formulas for the solution of the Hermite collocation discretization of a nonhomogeneous...

 

Link

Parallel Implementation of the Bi-CGSTAB Method with Block Red–Black Gauss–Seidel Preconditioner Applied to the Hermite Collocation Discretization of Partial Differential Equations (with George F. Pinder), Parallel Computing (2002)

We describe herein the parallel implementation of the Bi-CGSTAB method with a block red–black Gauss–Seidel...

 

Analytical Solution of Hermite Collocation Discretization of Self-Adjoint Ordinary Differential Equations, International Journal of Differential Equations and Applications (2002)

We give herein analytical formulas for the solutions of a class of boundary value problems...

 

Analytical Solution of Hermite Collocation Discretization of the Steady-State Convection-Diffusion Equation, International Journal of Differential Equations and Applications (2002)

We give herein analytical formulas for the Hermite collocation solution of the steady-state convection-diffusion equation...

 

Optimal Upstream Collocation Solution of the One-Dimensional Steady-State Convection-Diffusion Equation, International Journal of Applied Mathematics and Computer Science (2002)

We give herein analytical formulas for the solution of the Hermite collocation discretization of the...

 

Link

Analysis of a Block Red-Black Preconditioner Applied to the Hermite Collocation Discretization of a Model Parabolic Equation (with George F. Pinder), Numerical Methods for Partial Differential Equations (2001)

We are concerned with the numerical solution of a model parabolic partial differential equation (PDE)...

 

Link

Eigenvalue Analysis of a Block Red-Black Gauss–Seidel Preconditioner Applied to the Hermite Collocation Discretization of Poisson's Equation (with George F. Pinder), Numerical Methods for Partial Differential Equations (2001)

This article is concerned with the numerical solution of Poisson's equation with Dirichlet boundary conditions,...

 

Hermite Collocation Solution of Partial Differential Equations via Preconditioned Krylov Methods, Numerical Methods for Partial Differential Equations (2001)

We are concerned with the numerical solution of partial differential equations (PDEs) in two spatial...

 

Presentations

Link

A New Basis for the Solution of the One-Dimensional Transport Equation, The XVI International Conference on Computational Methods in Water Resources (2006)

We present a family of functions that satisfy the one-dimensional convection-diffusion equation. This partial differential...