I just came across Total Variation Diminishing schemes, where it has been mentioned that for the scheme to be non-oscillating, the following criteria should be followed:

- the scheme should be monotonic preserving i.e.

- it must not create local extreme

- the value of an existing local minimum must be non-decreasing, and that of a local maximum must be non-increasing.

May someone elaborate or explain, how these are not obeyed on QUICK or Central difference (as these are only conditional TVD).

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