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==Computational Cost:==
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 [[FEM]] or [[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.
==Application of Finite Differences to ODE==
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