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Article
Analytical Solution of Hermite Collocation Discretization of the Steady-State Convection-Diffusion Equation
International Journal of Differential Equations and Applications
  • Stephen H. Brill, Boise State University
Document Type
Article
Publication Date
1-1-2002
Disciplines
Abstract
We give herein analytical formulas for the Hermite collocation solution of the steady-state convection-diffusion equation with constant coefficients defined on a uniform mesh in one spatial dimension. Both Dirichlet and Neumann boundary conditions are considered. Analysis is provided which compares the discrete collocation solution to the continuous solution. Unlike the solution obtained via the central difference discretization, the collocation solution is proven to be oscillation free, irrespective of the value of the Péclet number. For modest Péclet numbers, the collocation solution is shown to provide an excellent approximation to the solution of the continuous problem.
Citation Information
Stephen H. Brill. "Analytical Solution of Hermite Collocation Discretization of the Steady-State Convection-Diffusion Equation" International Journal of Differential Equations and Applications (2002)
Available at: http://works.bepress.com/stephen_brill/4/