Publication Type

Journal Article

Version

acceptedVersion

Publication Date

5-2003

Abstract

The δ-type discrete singular convolution (DSC) algorithm has recently been proposed and applied to solve kinds of partial differential equations (PDEs). With appropriate parameters, particularly the key parameter r in its regularized Shannon's kernel, the DSC algorithm can be more accurate than the pseudospectral method. However, it was previously selected empirically or under constrained inequalities without optimization. In this paper, we present a new energy-minimization method to optimize r for higher-order DSC algorithms. Objective functions are proposed for the DSC algorithm for numerical differentiators of any differential order with any discrete convolution width. Typical optimal parameters are also shown. The validity of the proposed method as well as the resulted optimal parameters have been verified by extensive examples.

Keywords

Discrete singular convolutions, Energy minimization, Numerical differentiators, Objective functions, Parameter optimization, Regularized Shannon's kernels

Discipline

Physical Sciences and Mathematics

Research Areas

Quantitative Finance

Publication

Communications in Numerical Methods in Engineering

Volume

19

Issue

5

First Page

377

Last Page

386

ISSN

1069-8299

Identifier

10.1002/cnm.596

Publisher

Wiley

Additional URL

https://doi.org/10.1002/cnm.596

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