This paper explores the utility, tests the accuracy and examines the limitation of the discrete singular convolution (DSC) algorithm for solving partial differential equations (PDEs). The standard Fourier pseudospectral (FPS) method is also implemented for a detailed comparison so that the performance of the DSC algorithm can be better evaluated. Three twodimensional PDEs of different nature, t...

This paper is pertained with the problem of admissibility analysis of uncertain discrete-time nonlinear singular systems by adopting the state-space Takagi-Sugeno fuzzy model with time-delays and norm-bounded parameter uncertainties. Lyapunov Krasovskii functionals are constructed to obtain delay-dependent stability condition in terms of linear matrix inequalities, which is dependent on the low...

A theory of singular and quasi-bounded temperatures associated with the heat equation is developed. Guided by the harmonic case [1] an operator S is defined on the set M of non-negative functions on an open set of Rn+l which admit superthermic majorants. Quasi-bounded and singular functions in M are defined from the operator S . The basic properties of S are discussed. Non-negative temperatures...

In[6], Hu and Yang obtain a variant sharp estimate for the multilinear singular integral operators. The main purpose of this paper is to prove a sharp inequality for some multilinear operators related to certain non-convolution type integral operators. In fact, we shall establish the sharp inequality for the multilinear operators only under certain conditions on the size of the integral operato...

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...

A new computational algorithm, the discrete singular convolution (DSC), is introduced for solving scattering and guided wave problems described by time-domain Maxwell s equations. The DSC algorithm is utilized for the spatial discretization and the fourth-order Runge–Kutta scheme is used for the time advancing. Staggered meshes are used for electromagnetic fields. Four standard test problems, a...

Observations depending on sums of random variables are common throughout many fields; however, no efficient solution is currently known for performing max-product inference on these sums of general discrete distributions (max-product inference can be used to obtain maximum a posteriori estimates). The limiting step to max-product inference is the max-convolution problem (sometimes presented in ...

A vectorial nonlocal and nonlinear parabolic problem on a bounded domain for an intermediate state between type-I and type-II superconductivity is proposed. The domain is for instance a multiband superconductor that combines the characteristics of both types. The nonlocal term is represented by a (space) convolution with a singular kernel arising in Eringen’s model. The nonlinearity is coming f...

This paper presents the effective control of the formation and competition of cellular patterns. Simulation and theoretical analyses are carried out for pattern formation in a confined circular domain. The Cahn–Hilliard equation is solved with the zero-flux boundary condition to describe the phase separation of binary mixtures. A wavelet-based discrete singular convolution algorithm is employed...