A Comparison Study of HO-CFD and DSC-RSK with Small Computational Bandwidths for Solving Some Classes of Boundary-Value and Eigenvalue Problems

Abstract

This paper conducts a comparison analysis of high order central finite difference (HO-CFD) method and discrete singular convolution-regularized Shannon kernel (DSC-RSK) scheme with small computational bandwidths for solving some classes of boundary-value and eigenvalue problems. Second-, fourth- and sixth-order partial differential equations are taken into account. New strategies to generate parameters [Formula: see text] in DSC-RSK are proposed to ensure minimum errors for each case, and the influence of parameters [Formula: see text] with more decimal places is analyzed. Apart from the existing matched interface and boundary (MIB) scheme, a new double-parameter MIB scheme is also proposed. The influence of small computational bandwidths is discussed in detail. Numerical results by using HO-CFD and DSC-RSK are presented and compared to illustrate the performance of both methods in small bandwidth limit. Some remarkable conclusions have been drawn at the end of this study.