A new method, combining complex analysis with numerics, is introduced for solving a large class of linear partial differential equations (PDEs). This includes any linear constant coefficient PDE, as well as a limited class of PDEs with variable coefficients (such as the Laplace and the Helmholtz equations in cylindrical coordinates). The method yields novel integral representations, even for th...

A generalized Cahn--Hilliard model in a bounded interval of the real line with no-flux boundary conditions is considered. The label ``generalized'' refers to fact that we consider concentration dependent mobility, $p$-Laplace operator $p > 1$ and double well potential form $F(u)=\frac{1}{2\theta}|1-u^2|^\theta$, $\theta 1$; these terms replace, respectively, constant linear Laplace $C^2$ satisf...

We study the equations governing a fluid loaded plate. We first reformu-late these equations as a system of two equations, one of which is an explicit non-local equation for the wave height and the velocity potential on the free surface. We then concentrate on the linearised equations and show that the problems formulated either on the full or the half line can be solved by employing the unifie...

We study the eigenvalues of the discrete Schrödinger operator with a complex potential. We obtain bounds on the total number of eigenvalues in the case where V decays exponentially at infinity.

Recently, various applications have motivated the study of spectral structures (eigenvalues and eigenfunctions) of the so-called Laplace-Beltrami operator of a manifold and their discrete versions. A popular choice for the discrete version is the so-called Gaussian weighted graph Laplacian which can be applied to point cloud data that samples a manifold. Naturally, the question of stability of ...

An upwind difference approximation is used for a singularly perturbed problem in material science. Based on the discrete Green’s function theory, the error estimate in maximum norm is achieved, which is first-order uniformly convergent with respect to the perturbation parameter. The numerical experimental result is verified the valid of the theoretical analysis. Keywords—singularly perturbed, u...

In this paper, we study a first order random coefficient autoregressive model with Laplace distribution as marginal. A random coefficient moving average model of order one with Laplace as marginal distribution is introduced and its properties are studied. By combining the two models, we develop a first order random coefficient autoregressive moving average model with Laplace marginal and discus...

Pseudo-Laplace transform is an important notion from pseudo-analysis’ framework that is often used in dealing with differential or integral equation. The (⊕, ̄)-Laplace transform considered here is a generalization of the pseudo-Laplace transform based on a special class of generalized pseudo-operations that need not be commutative nor associative. This pseudo-Laplace type transform has been use...

Ab initio calculations of the shapes of pure CO2 infrared and Raman bands under (pressure) conditions for which line-mixing effects are important have been performed using requantized classical molecular dynamics simulations. This approach provides the autocorrelation functions of the dipole vector and isotropic polarizability whose Fourier-Laplace transforms yield the corresponding spectra. Fo...