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The [[CPU]] time to solve the system of equations differs substantially from method to method. Finite differences are usually the cheapest on a per grid point basis followed by the finite element method and spectral method. However, a per grid point basis comparison is a little like comparing apple and oranges. Spectral methods deliver more accuracy on a per grid point basis than either [[Finite element method|FEM]] or [[Finite difference method|FDM]]. The comparison is more meaningful if the question is recast as ”what is the computational cost to achieve a given error tolerance?”. The problem becomes one of defining the error measure which is a complicated task in general situations.
==<s><ref>{{Cite news|others=John Locke|title=}}</ref></s>Forward Euler approximation==
:<math> \frac {u^{n+1} -u^n}{\Delta t } \approx \kappa u^n </math>
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