Related Directory Categories
Sources
open directory project
Help build the largest human-edited directory on the web.
Submit a site - Become an editor
Wikipedia. Licensed under the GNU Free Documentation License.
Are you an expert in this subject? Join the discussion and share your knowledge at Wikipedia.org.
Numerical partial differential equations
From Wikipedia, the free encyclopedia
Numerical partial differential equations is the branch of numerical analysis that studies the numerical solution of partial differential equations (PDEs).
Numerical techniques for solving PDEs include the following:
- The finite difference method, in which functions are represented by their values at certain grid points and derivatives are approximated through differences in these values.
- The finite element method, where functions are represented in terms of basis functions and the PDE is solved in its integral (weak) form.
- The finite volume method, which divides space into regions or volumes and computes the change within each volume by considering the flux (flow rate) across the surfaces of the volume.
- The spectral method, which represents functions as a sum of particular basis functions, for example using a Fourier series.
The finite difference method is often regarded as the simplest method to learn and use. The finite element and finite volume methods are widely used in engineering and in computational fluid dynamics, and are well suited to problems in complicated geometries. Spectral methods are generally the most accurate, provided that the solutions are sufficiently smooth.
- finite difference
- finite element method
- finite volume method
- spectral method
- Numerical ordinary differential equations
- Numerical Methods for Partial Differential Equations course at MIT OpenCourseWare.
- IMS, the Open Source IMTEK Mathematica Supplement (IMS)
 |
This mathematics-related article is a stub. You can help Wikipedia by expanding it. |