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Dehghan, M. (2005) On the Numerical Solution of the One-Dimensional Convection-Diffusion Equation. Mathematical Problems in Engineering, 2005, 61-74.
https://doi.org/10.1155/mpe.2005.61

has been cited by the following article:

• TITLE: Higher Order Approximation of Advection Diffusion Equation by Semi-Discretization Method

  AUTHORS: Khandoker Nasrin Ismet Ara, Md. Sabbir Alam, Laek Sazzad Andallah

  KEYWORDS: Advection Diffusion Equation, Semi-Discretization, Finite Difference Scheme, Rate of Convergence, System of ODE’s

  JOURNAL NAME: American Journal of Computational Mathematics, Vol.15 No.3, July 30, 2025

  ABSTRACT: A system of ordinary differential equations (ODEs) is produced by the semi-discretize method of discretizing the advection diffusion equation (ADE). Runge-Kutta methods of the second and fourth orders are used to solve the system of ODEs. We compute the ADE numerically for initial and boundary conditions, for which the exact solution is known. In the semi-discretization approach, we estimate the error for both the second and fourth-order Runge-Kutta schemes. The semi-discretization method’s outcome is contrasted with the ADE’s numerical solution derived from the complete discretization explicit centered difference scheme.