Recently, Boyd published a paper entitled ‘‘A proof that the discrete singular convolution (DSC)/ Lagrange-distributed approximating function (LDAF) method is inferior to high order finite differences’’ (J. Comput. Phys. 214 (2006) 538–549 [3]), which will be referred to as ‘‘Proof’’. This Letter analyzes the validity of central claims in ‘‘Proof’’. In its title and abstract, ‘‘Proof’’ refers t...

*Correspondence: [email protected] School of Mathematical Science, Qufu Normal University, Jingxuanxi Road 57, Qufu, Shandong 273165, P.R. China Abstract One class of singular integral equations of convolution type with Hilbert kernel is studied in the space L2[–π ,π ] in the article. Such equations can be changed into either a system of discrete equations or a discrete jump problem depending o...

This paper proposes a Hermite-kernel realization of the conjugate filter oscillation reduction (CFOR) scheme for the simulation of fluid flows. The Hermite kernel is constructed by using the discrete singular convolution (DSC) algorithm, which provides a systematic generation of low-pass filter and its conjugate high-pass filters. The high-pass filters are utilized for approximating spatial der...