Applied Mathematical Sciences, Vol. 7, 2013, no. 35, 1737 - 1755 HIKARI Ltd, www.m-hikari.com The Finite Volume Method for Solving Systems of Non-linear Initial-Boundary Value Problems for PDE's 1 Eman Ali Hussain and 2 Zainab Mohammed Alwan 1 Department of Mathematics, College of Science University of AL- Mustansiriyah, Iraq dr_emansultan@yahoo.com 2 Department of Mathematics, College of Science University of AL- Mustansiriyah, Iraq lionwight_2009@yahoo.com Copyright © 2013 Eman Ali Hussain and Zainab Mohammed Alwan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract This paper concerned the finite volume method that applied to solve some kinds of systems of non-linear boundary value problems (elliptic, parabolic and hyperbolic) for PDE's. Keywords: Finite Volume Method, Control Volume, System, Boundary Value Problems 1. Introduction One of the most important sources in applied mathematics is the boundary value problems, such as mathematical models, biology (the rate of growth of microorganism), [1], chemical engineering (an exothermic chemical reaction , heat conduction associated with radiation effects, deformation of shells), [10], heat and mass transfer or petroleum engineering, tools for scientific computing, [7]. Generally speaking, a boundary value problem consists of an equation with boundary conditions.