Finite Volume method is mostly used in CFD to evaluate the PDEs which become the form of algebraic equations. These types of equations are solved by matrix techniques or by numerical methods. In this work we have used Tri-Diagonal Matrix Algorithm to get solution of 2D Convection –Diffusion Equation. Which is capable for mesh problems. It applies line by line mesh nodes. We have worked with time dependent problem so, for this purpose researchers are used LSRK method to decrease the time step but our work is not to deal with step size. Our work is dependent upon stability analysis of solution. For this motive we have used central scheme and peclet number at different value of gamma. Stability of solution in this work dependent upon peclet number. When peclet number goes greater than 2 then our solution become unstable.

Keywords: Convection and Diffusion Equations, Central Scheme,Low storage Explicit RK method, Stability of Finite Volume Method, Tri-Diagonal Matrix Algorithm.