Numerical Solution of Convection–Diffusion Equation Using Cubic B-Spline Quasi-Interpolation

Hossein Aminikhah, Javad Alavi

Abstract

In this paper, the convection-diffusion equation with Dirichlet's type boundary conditions is solved numerically by cubic B-spline quasi-interpolation. The numerical scheme, obtained by using the derivative of the quasi-interpolation to approximate the spatial derivative of the dependent variable and first order forward difference to approximate the time derivative of the dependent variable. The developed method is tested on various problems and the numerical results are reported in tabular and graphical form. Easy and economical implementation process is the strength of the scheme. The results of numerical experiments are compared with analytical solutions by calculating errors $L_{2}$, $L_{\infty}$-norms.