8. Numerical Methods
Published Online: 4 APR 2013
Copyright © 2013 by John Wiley & Sons, Inc.
Applied Diffusion Processes from Engineering to Finance
How to Cite
Janssen, J., Manca, O. and Manca, R. (2013) Numerical Methods, in Applied Diffusion Processes from Engineering to Finance, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/9781118578339.ch8
- Published Online: 4 APR 2013
- Published Print: 4 MAR 2013
Print ISBN: 9781848212497
Online ISBN: 9781118578339
- finite differences method;
- numerical methods;
- partial differential equations (PDE)
The numerical methods useful for partial differential equations (PDEs) solutions present a continuous improvement. Usually, numerical solutions used for PDE are finite differences methods (FDMs), finite volume methods (FVMs) or finite elements methods (FEMs) that approximate PDE by means of algebraic equations. It is noted that the system matrix obtained by solving the PDE by means of FDM is sparse, usually non-symmetric, but topologically symmetric. This chapter proposes algorithms that are useful for the solutions that come from FDMs. The discretization of the domain is the first step to transform a PDE in a finite difference system.