A benchmark quality solution is presented for ow in a staggered double lid driven cavity obtained by using the wavelet-based discrete singular convolution (DSC). The proposed wavelet based algorithm combines local methods’ exibility and global methods’ accuracy, and hence, is a promising approach for achieving the high accuracy solution of the Navier–Stokes equations. Block structured grids wit...

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...

We present two numerical methods for the approximation of the generalized Zakharov system (ZS). The first one is the time-splitting spectral (TSSP) method, which is explicit, time reversible, and time transverse invariant if the generalized ZS is, keeps the same decay rate of the wave energy as that in the generalized ZS, gives exact results for the plane-wave solution, and is of spectral-order...

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...

A vectorial nonlocal linear hyperbolic problem with applications in superconductors of type-I is studied. The nonlocal term is represented by a (space) convolution with a singular kernel, which is arising in Eringen’s model. The well-posedness of the problem is discussed under low regularity assumptions and the error estimates for two time-discrete schemes (based on backward Euler approximation...

We investigate pinning regions and unpinning asymptotics in nonlocal equations. We show that phenomena are related to but different from pinning in discrete and inhomogeneous media. We establish unpinning asymptotics using geometric singular perturbation theory in several examples. We also present numerical evidence for the dependence of unpinning asymptotics on regularity of the nonlocal convo...