High-order compact boundary value method for the solution of unsteady convection-diffusion problems

Authors:
Mehdi Dehghan;Akbar Mohebbi
Affiliations:
Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, No. 424 Hafez Avenue, 15914 Tehran, Iran;Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, No. 424 Hafez Avenue, 15914 Tehran, Iran
Venue:
Mathematics and Computers in Simulation
Year:
2008

Citing 9
Cited 1

Stability properties of some boundary value methods

Applied Numerical Mathematics
Stability of some boundary value methods for IVPs

NUMDIFF-7 Selected papers of the seventh conference on Numerical treatment of differential equations
High-order compact-difference schemes for time-dependent Maxwell equations

Journal of Computational Physics
Block-Boundary Value Methods for the Solution of Ordinary Differential Equations

SIAM Journal on Scientific Computing
Determination of a control parameter in the two-dimensional diffusion equation

Applied Numerical Mathematics
High order ADI method for solving unsteady convection-diffusion problems

Journal of Computational Physics
High order finite difference numerical methods for time-dependent convection-dominated problems

Applied Numerical Mathematics - Applied scientific computing: Recent approaches to grid generation, approximation and numerical modelling
Finite difference procedures for solving a problem arising in modeling and design of certain optoelectronic devices

Mathematics and Computers in Simulation
A fourth-order compact ADI method for solving two-dimensional unsteady convection-diffusion problems

Journal of Computational and Applied Mathematics

High-order solution of one-dimensional sine-Gordon equation using compact finite difference and DIRKN methods

Mathematical and Computer Modelling: An International Journal

Quantified Score

Hi-index	0.00

Visualization

Abstract

In this paper, we propose a new class of high-order accurate methods for solving the two-dimensional unsteady convection-diffusion equation. These techniques are based on the method of lines approach. We apply a compact finite difference approximation of fourth order for discretizing spatial derivatives and a boundary value method of fourth order for the time integration of the resulted linear system of ordinary differential equations. The proposed method has fourth-order accuracy in both space and time variables. Also this method is unconditionally stable due to the favorable stability property of boundary value methods. Numerical results obtained from solving several problems include problems encounter in many transport phenomena, problems with Gaussian pulse initial condition and problems with sharp discontinuity near the boundary, show that the compact finite difference approximation of fourth order and a boundary value method of fourth order give an efficient algorithm for solving such problems.