Difference between revisions of "NumMethodsPDEs"
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<math> Au_{xx} + Bu_{xy} + Cu_{yy} + Du_x + Eu_y + Fu = G </math> | <math> Au_{xx} + Bu_{xy} + Cu_{yy} + Du_x + Eu_y + Fu = G </math> | ||
| + | |||
| + | * '''Parabolic''' | ||
| + | * '''Hyperbolic''' | ||
| + | * '''Elliptic''' | ||
Revision as of 17:22, 17 January 2011
Numerical Methods for PDEs: Solving PDEs on a computer
Introduction
Looking at Nature
A second-order linear equation in two variables:
[math]\displaystyle{ Au_{xx} + Bu_{xy} + Cu_{yy} + Du_x + Eu_y + Fu = G }[/math]
- Parabolic
- Hyperbolic
- Elliptic
[math]\displaystyle{ f(x + h) = f(x) + \frac{f'(x)}{1!}h + \frac{f^{(2)}(x)}{2!}h^2 + \cdots + \frac{f^{(n)}(x)}{n!}h^n + R_n(x) }[/math]