A numerical method for diffusion–convection equation using high-order difference schemes

In this paper, we propose a simple general form of high-order approximation of O(c2+ch2+h4)O(c2+ch2+h4) to solve the two-dimensional parabolic equation αuxx+βuyy=F(x,y,t,u,ux,uy,ut)αuxx+βuyy=F(x,y,t,u,ux,uy,ut), where α and β are positive constants. We apply the compact form for solving diffusion–convection equation. The results of numerical experiments are presented and compared with analytical solutions to confirm the higher accuracy of the presented scheme.