PDEs
A partial differential equation (PDE) extends ODEs by adding
one or more independent variables (usually spatial variables). For
example, the wave equation for the ideal vibrating string adds one
spatial dimension (along the axis of the string) and may be written as
follows:
![]() ![]() |
(2.1) |
where
![$ y(x,t)$](http://www.dsprelated.com/josimages_new/pasp/img182.png)
![$ x$](http://www.dsprelated.com/josimages_new/pasp/img179.png)
![$ t$](http://www.dsprelated.com/josimages_new/pasp/img122.png)
![$ y'(x,t)\isdeftext \partial y(x,t)/\partial x$](http://www.dsprelated.com/josimages_new/pasp/img183.png)
![$ y$](http://www.dsprelated.com/josimages_new/pasp/img184.png)
![$ x$](http://www.dsprelated.com/josimages_new/pasp/img179.png)
![$ K$](http://www.dsprelated.com/josimages_new/pasp/img185.png)
![$ \epsilon $](http://www.dsprelated.com/josimages_new/pasp/img186.png)
Next Section:
Difference Equations (Finite Difference Schemes)
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ODEs