In numerical analysis and applied mathematics, sinc numerical methods are numerical techniques for finding approximate solutions of partial differential equations and integral equations based on the translates of sinc function and Cardinal function C(f,h) which is an expansion of f defined by
formula_1
where the step size h ;0 and where the sinc function is defined by
formula_2
Sinc approximation methods excel for problems whose solutions may have singularities, or infinite domains, or boundary layers.
The truncated Sinc expansion of f is defined by the following series:
formula_3 .
Sinc numerical methods cover.
Indeed, Sinc are ubiquitous for approximating every operation of calculus
In the standard setup of the sinc numerical methods, the errors (in big O notation) are known to be formula_4 with some c ;0, where n is the number of nodes or bases used in the methods. However, Sugihara has recently found that the errors in the Sinc numerical methods based on double exponential transformation are formula_5 with some k ;0, in a setup that is also meaningful both theoretically and practically and are found to be best possible in a certain mathematical sense.
References.
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