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A First Course in the Numerical Analysis of Differential Equations by Arieh Iserles

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16

The diffusion equation

16.1  simple numerical method

It is often useful to classify partial differential equations into two kinds: steady-state equations, where all the variables are spatial, and evolutionary equations, which combine differentiation with respect to space and to time. We have already seen some examples of steady-state equations, namely the Poisson equation and the biharmonic equation. Typically, equations of this type describe physical phenomena whose behaviour depends on the minimization of some quantity, e.g. potential energy, ...

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