Encyclopedia of Systems Biology

2013 Edition
| Editors: Werner Dubitzky, Olaf Wolkenhauer, Kwang-Hyun Cho, Hiroki Yokota

Partial Differntial Equations, Numerical Methods and Simulations

Reference work entry
DOI: https://doi.org/10.1007/978-1-4419-9863-7_293



Partial differential equations (PDEs) form the basis for modeling numerous complex phenomena in systems biology. A PDE typically relates a function of several independent variables with its partial derivatives with respect to the independent variables (Evans 1998; Kevorkian 1993). PDEs are traditionally classified in terms of their order (the highest order derivative in the PDE) and degree (the degree of the highest order derivative in the PDE) and whether they are linear or nonlinear. However, the basic structure of a PDE generally depends on the type of problem involved in a particular application. In systems biology applications (e.g., modeling blood flow in cardiovascular systems and other biofluid flow models; modeling advective-diffusive transport of biochemical species in blood; modeling coupled blood-tissue transport and metabolism in an organ; natural pattern formation models;...

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© Springer Science+Business Media, LLC 2013

Authors and Affiliations

  1. 1.Department of PhysiologyBiotechnology and Bioengineering Center, Medical College of WisconsinMilwaukeeUSA