We study a generalized extrapolated Crank–Nicolson scheme for the time discretization of a semilinear integro-differential equation with a weakly singular kernel, in combination with a space discretization by linear finite elements. The scheme uses variable grids in time to compensate for the singular behaviour of the exact solution at t = 0. With appropriate assumptions on the data and assumin...

This paper proposes a novel meshless boundary method called the singular boundary method (SBM). This method is mathematically simple, easy-to-program, and truly meshless. Like the method of fundamental solutions (MFS), the SBM employs the singular fundamental solution of the governing equation of interest as the interpolation basis function. However, unlike the MFS, the source and collocation p...

The paper describes an analytical tool in MATLAB for determining the nature of the stress and displacement fields near a fairly general singular point in linear elasticity. The user is prompted to input the local geometry of the system, the material properties, and the boundary conditions (and interface conditions in the case of composite bodies or problems involving contact between two or more...

Discourses are linguistic structures above sentence level. Discourse is nothing but a coherent sequence of sentences. Discourse analysis is concerned with coherent processing of text segments larger than the sentence and this requires something more than just the interpretation of the individual sentences. A phenomenon that operates at discourse level includes cohesion. Text is cohesive if its ...

We consider the approximation of systems of singularly perturbed reaction-diffusion equations, with the finite element method. The solution to such problems contains, in general, boundary layers which overlap and interact, and the numerical approximation must take this into account in order for the resulting scheme to converge uniformly with respect to the singular perturbation parameters. In t...

We introduce a nonconforming finite-element method for second order elliptic interface problems. Our approach applies to problems in which discontinuous coefficients and singular sources on the interface may give rise to jump discontinuities in either the solution or its normal derivative. Given a standard background mesh and an interface that passes between elements, the key idea is to constru...

    M. and M.   Abstract: Existence and uniqueness of solution for singular 2-D systems depends on regularity condition. Simple regularity implies regularity and under this assumption, the generalized wave model (GWM) is introduced to cast singular 2-D system of equations as a family of non-singular 1-D models with variable structure.These index dependent models, along with a set of boundary co...

The present paper deals with a boundary element formulation based on the traction elasticity boundary integral equation (potential derivative for Laplace’s problem). The hypersingular and strongly singular integrals appearing in the formulation are analytically transformed to yield line and surface integrals which are at most weakly singular. Regularization and analytical transformation of the ...

Abstract: We study the level spacing distribution P (S) of 2D real random matrices both symmetric as well as general, non-symmetric. In the general case we restrict ourselves to Gaussian distributed matrix elements, but different widths of the various matrix elements are admitted. The following results are obtained: An explicit exact formula for P (S) is derived and its behaviour close to S = 0...