8. Numerical Methods

  1. Jacques Janssen,
  2. Oronzio Manca and
  3. Raimondo Manca
  1. Jacques Janssen,
  2. Oronzio Manca and
  3. Raimondo Manca

Published Online: 4 APR 2013

DOI: 10.1002/9781118578339.ch8

Applied Diffusion Processes from Engineering to Finance

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

Publication History

  1. Published Online: 4 APR 2013
  2. Published Print: 4 MAR 2013

ISBN Information

Print ISBN: 9781848212497

Online ISBN: 9781118578339

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Keywords:

  • discretization;
  • finite differences method;
  • numerical methods;
  • partial differential equations (PDE)

Summary

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.