Numerical Solution of Convection-Diffusion Equation with the Help of Viscous Burger’s Equation

T M A K Azad
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T M A K Azad: Department of Computer Science & Engineering, University of Liberal Arts Bangladesh, Dhaka-1209

International Journal of Research and Innovation in Applied Science, 2025, vol. 10, issue 2, 103-116

Abstract: Two finite difference schemes, FTBSCS (forward time backward space and centered space) and FTCS (forward time centered space) have been studied for solving convection-diffusion equation (CDE) with appropriate initial condition and boundary conditions. The convection velocity u(t, x) of CDE is computed by solving viscous Burger’s equation using the same schemes. Stability conditions of the schemes are determined and it is analytically shown that FTCS scheme is superior to FTBSCS scheme in terms of time step selection. The conditions of stability are also numerically verified. Some numerical simulation results are presented for various parameters. Error comparisons of both the schemes are presented to estimate accuracy of solutions.

Date: 2025
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