Abstract. We will achieve new configuration of the analytical solutions to the reaction-convection-diffusion equation (RCDE) which possess a significant role in mathematical physics applications and biological science. These new configurations of the analytical solution have been documented via the Paul-Painlevé approach method (PPAM) and the (G’/G)-expansion method. These two techniques are used for the first time to achieve these new configurations of the analytical solution of this equation. In addition, the numerical solutions analogous to all achieved analytical solutions have been detected via the variational iteration method (VIM) that usually gives good numerical solutions.

Key words: reaction-convection-diffusion equation, Paul-Painlevé approach method, traveling wave solutions, numerical solutions.