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Unequal intervals derivative approximations

Higher-order methods Chap. 9, Sect. 9.2.2 for multipoint discretisations. The four-point variant with unequal intervals is probably optimal the system can be solved using an extended Thomas algorithm without difficulty. Numerov methods (Sect. 9.2.7) can achieve higher orders with only three-point approximations to the spatial second derivative. They are not trivial to program. [Pg.271]

This program is again a Cottrell simulation using second-order extrapolation based on the Bl (Laasonen) method and unequal intervals, but in contrast with the above program C0TT EXTRAP, this one makes use of the four-point spatial derivative approximation, and the GU-function. It performs a little better than the above program, at little extra programming effort. [Pg.308]

There are different improvements that can be included in the different methods presented here. Thus, multi-point approximations to the derivatives [1], the use of unequally spaced spatial and time intervals [1, 8,9], and the use of more sophisticated methods of time integration [1], among others, have been developed. [Pg.652]

After introducing unequal spatial intervals, the finite differences must be reformulated. Following the central three-point approximation introduced in Chapter 3, the second derivative can be approximated as... [Pg.74]

The basic principle in using the finite difference method to solve BVPs is to replace all the derivatives in the differential equation with difference-quotient approximations. First, the interval a < x < b is discretized into n equally spaced intervals (an unequal spaced interval may also be used) ... [Pg.102]


See other pages where Unequal intervals derivative approximations is mentioned: [Pg.139]    [Pg.215]    [Pg.269]    [Pg.129]    [Pg.168]    [Pg.412]    [Pg.104]    [Pg.52]    [Pg.124]    [Pg.130]    [Pg.138]   
See also in sourсe #XX -- [ Pg.282 , Pg.283 ]

See also in sourсe #XX -- [ Pg.440 ]




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Unequal

Unequal intervals

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