Optimal Collocation Solution of the One-Dimensional Steady-State Convection-Diffusion Equation with Variable Coefficients

Stephen H. Brill

Optimal Collocation Solution of the One-Dimensional Steady-State Convection-Diffusion Equation with Variable Coefficients

Stephen H. Brill

Mathematics Department

Research output: Contribution to journal › Article › peer-review

Abstract

We study the Hermite collocation solution of the one-dimensional-steady-state convection-diffusion equation with Dirichlet boundary conditions. The diffusion coefficient is constant while the convection coefficient is piecewise contant. A uniform mesh is imposed on each portion of the domain on which the convection coefficient is constant, but each portion may have a different uniform mesh. Formulas are derived for the exact solution of the matrix equation that arises from the collocation discretization. These formulas possess free "upstreaming/downstreaming" parameters, the values of which may be chosen to yield numerical solutions of great accuracy.

Original language	American English
Journal	International Journal of Computational and Numerical Analysis and Applications
State	Published - 1 Jan 2004

Keywords

collocation
convection-diffusion
exact solution
upstream
variable coefficients

EGS Disciplines

Mathematics

Cite this

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title = "Optimal Collocation Solution of the One-Dimensional Steady-State Convection-Diffusion Equation with Variable Coefficients",

abstract = " We study the Hermite collocation solution of the one-dimensional-steady-state convection-diffusion equation with Dirichlet boundary conditions. The diffusion coefficient is constant while the convection coefficient is piecewise contant. A uniform mesh is imposed on each portion of the domain on which the convection coefficient is constant, but each portion may have a different uniform mesh. Formulas are derived for the exact solution of the matrix equation that arises from the collocation discretization. These formulas possess free {"}upstreaming/downstreaming{"} parameters, the values of which may be chosen to yield numerical solutions of great accuracy.",

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year = "2004",

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TY - JOUR

T1 - Optimal Collocation Solution of the One-Dimensional Steady-State Convection-Diffusion Equation with Variable Coefficients

AU - Brill, Stephen H.

PY - 2004/1/1

Y1 - 2004/1/1

N2 - We study the Hermite collocation solution of the one-dimensional-steady-state convection-diffusion equation with Dirichlet boundary conditions. The diffusion coefficient is constant while the convection coefficient is piecewise contant. A uniform mesh is imposed on each portion of the domain on which the convection coefficient is constant, but each portion may have a different uniform mesh. Formulas are derived for the exact solution of the matrix equation that arises from the collocation discretization. These formulas possess free "upstreaming/downstreaming" parameters, the values of which may be chosen to yield numerical solutions of great accuracy.

AB - We study the Hermite collocation solution of the one-dimensional-steady-state convection-diffusion equation with Dirichlet boundary conditions. The diffusion coefficient is constant while the convection coefficient is piecewise contant. A uniform mesh is imposed on each portion of the domain on which the convection coefficient is constant, but each portion may have a different uniform mesh. Formulas are derived for the exact solution of the matrix equation that arises from the collocation discretization. These formulas possess free "upstreaming/downstreaming" parameters, the values of which may be chosen to yield numerical solutions of great accuracy.

KW - collocation

KW - convection-diffusion

KW - exact solution

KW - upstream

KW - variable coefficients

UR - https://scholarworks.boisestate.edu/math_facpubs/79

M3 - Article

JO - International Journal of Computational and Numerical Analysis and Applications

JF - International Journal of Computational and Numerical Analysis and Applications

ER -

Optimal Collocation Solution of the One-Dimensional Steady-State Convection-Diffusion Equation with Variable Coefficients

Abstract

Keywords

EGS Disciplines

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