In numerical analysis and applied mathematics, sinc numerical methods are numerical techniques[1] 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 where the step size h>0 and where the sinc function is defined by 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: 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
with some c>0, where n is the number of nodes or bases used in the methods.
However, Sugihara[2] has recently found that the errors in the Sinc numerical methods based on double exponential transformation are
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.