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....

A novel discrete singular convolution (DSC)  formulation  is  presented for the seepage analysis in irregular geometric porous media. The DSC is a new promising numerical approach which has been recently applied to solve several engineering problems. For a medium with regular geometry, realizing of the DSC for the seepage analysis is straight forward. But DSC implementation for a medium with ir...

The Gaussian scale-space is a singular integral convolution operator with scaled Gaussian kernel. For a large class of singular integral convolution operators with differentiable kernels, a general method for constructing mother wavelets for continuous wavelet transforms is developed, and Calderón type inversion formulas, in both integral and semi-discrete forms, are derived for functions in L ...

In this paper, Lagrange interpolation in Chebyshev-Gauss-Lobatto nodes is used to develop a procedure for finding discrete and continuous approximate solutions of a singular boundary value problem. At first, a continuous time optimization problem related to the original singular boundary value problem is proposed. Then, using the Chebyshev- Gauss-Lobatto nodes, we convert the continuous time op...

This paper introduces a discrete singular convolution algorithm for solving the Fokker–Planck equation. Singular kernels of the Hilbert-type and the delta type are presented for numerical computations. Various sequences of approximations to the singular kernels are discussed. A numerical algorithm is proposed to incorporate the approximation kernels for physical applications. Three standard pro...

Static analysis of shear deformable plates resting on two-parameter foundations is presented by the method of discrete singular convolution (DSC). The influence of foundation parameters on the deflections of the plate has been investigated. Numerical studies are performed and the DSC results are compared well with other analytical solutions and some numerical results.

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...

This paper explores the connection between wavelet methods and an efficient computational algorithm—the discrete singular convolution (DSC). Many new DSC kernels are constructed and they are identified as wavelet scaling functions. Two approaches are proposed to generate wavelets from DSC kernels. Two well known examples, the Canny filter and the Mexican hat wavelet, are found to be special cas...