This material is taught in the BSc. Mathematics degree programme at the Manchester Metropolitan University, UK. The Finite Volume Method (FVM) is taught after the Finite Difference Method (FDM) where important concepts such as convergence, consistency and stability are presented. The FDM material is contained in the online textbook, ‘Introductory Finite Difference Methods for PDEs’ which is free to download from this website

It is recommended that the FDM text book is read before this book. This textbook is also freely downloadable from the above website.

The following chapters contain core material supported by pen and paper exercises together with computer-based exercises where appropriate. Supporting material, including worked solutions, and computer codes can be found at the companion website:

www2.docm.mmu.ac.uk/STAFF/C.Mingham

Codes, with which the student can experiment, are written using Matlab. In the spirit of Open Source, it is hoped to reproduce these codes using Scilab (a Matlab clone, downloadable for free from www.scilab.org).

The emphasis of this book is on a practical understanding of the basics of the FVM and a minimum of theory is given to underpin the method. Revision material is provided in appendices. It is recommended that anyone wishing to use the FVM to solve systems of equations for real world applications reads up on the underlying physics of the problem.

This book is intended for final year undergraduates who have knowledge of Calculus, vectors and introductory level computer programming.