This paper explores the utility of a discrete singular convolution algorithm for vibration analysis. A number of di!erent realizations of singular convolution kernels are selected to illustrate the present algorithm. Vibration analysis of strings, rods, beams, diatomic molecules, membranes, waveguides and thin plates are utilized to test numerical accuracy and speed of convergence of the presen...

This paper explores the utility of a discrete singular convolution (DSC) algorithm for the integration of the sine-Gordon equation. The initial values are chosen close to a homoclinic manifold for which previous methods have encountered significant numerical difficulties such as numerically induced spatial and temporal chaos. A number of new initial values are considered, including a case where...

In this paper, a discrete singular convolution (DSC) algorithm is introduced to solve Fisher’s equation, to which obtaining an accurate and reliable traveling wave solution is a challenging numerical problem. Two novel numerical treatments, a moving frame scheme and a new asymptotic scheme, are designed to overcome the subtle difficulties involved in the numerical solution of Fisher’s equation....

This paper explores the potential of a newly developed conjugate lter oscillation reduction (CFOR) scheme for shock-capturing under the in uence of natural high-frequency oscillations. The conjugate lowand high-pass lters are constructed based on the principle of the discrete singular convolution (DSC), a local spectral method. The accuracy and resolution of the DSC basic algorithm are accessed...

This paper explores the utility of a discrete singular convolution (DSC) algorithm for solving the Black–Scholes equation. Both European and American style options, which include all nontrivial plain option pricing problems, are considered to test the accuracy and to examine the efficiency of the present algorithm. Adaptive meshes are constructed to enhance the performance of the DSC algorithm....

This paper introduces the discrete singular convolution (DSC) algorithm for edge detection. Two classes of new edge detectors, DSC edge detector (DSCED) and DSC anti-noise edge detector (DSCANED), are proposed for the detection of multiscale edges. The DSCED is capable of extracting the 4ne details of images, whereas DSCANED is robust against noise. The combination of two classes of DSC edge de...

Membranes are widely used in various engineering applications such as the design stage of microphones, pumps, pressure regulators, and other acoustical applications. This paper investigates the numerical aspects for free vibration analysis of homogeneous and nonhomogeneous rectangular and square membranes. The method of discrete singular convolution is employed. The results are obtained for dif...

A class of local spectral wavelet filters, discrete singular convolution (DSC) filters, is utilized to facilitate the Fourier pseudospectral method for the solution of hyperbolic conservation law systems. The DSC lowpass filters are adaptively implemented directly in the Fourier domain (i.e., windowed Fourier pseudospectral method), while a physical domain algorithm is also given to enable the ...

This paper addresses a challenging problem in computational mechanics—the analysis of thick shallow shells vibrating at high modes. Existing methods encounter significant difficulties for such a problem due to numerical instability. A new numerical approach, DSC-Ritz method, is developed by taking the advantages of both the discrete singular convolution (DSC) wavelet kernels of the Dirichlet ty...