The convection diffusion reaction equation was solved using pseudo-spectral methods with direct solution for constant coefficients and convolutions for variable coefficients. Additionally, different integration methods were tested for the solution accuracy and stability with changing Peclet number including self-implemented 2nd and 4th order Runge Kutta methods, semi-implicit methods, Rosenberg methods and the Radau and Runge Kutta Methods from the Python library. The implicit fourth order Radau method gives the most accuracy and stability for the simulation.