reduced differental transform method (rdtm), which isone of the useful and effective numerical method, is applied to solve nonlinear time-dependent foam drainage equation (fde) with different initial conditions. we compare our method with the famous adomian decomposition and laplace decomposition methods. the obtained resultsdemonstrated that rdtm is a powerful tool for solving nonlinear par...

The well-known Laplace–Beltrami operator, established as a basic tool in shape processing, builds on a long history of mathematical investigations that have induced several numerical models for computational purposes. However, the Laplace–Beltrami operator is only one special case of many possible generalizations that have been researched theoretically. Thereby it is natural to supplement some ...

2 ABSTRACT A preliminary study was conducted with the message passing library PVM for the iterative solution of a two-dimensional Laplace equation. A line iterative procedure and Stone's strongly implicit solution procedure were tested in this environment as they have direct applicability to the solution of the pressure-Poisson equation. The intent of this study was not so much to study the sol...

We consider the Laplace transform as a Henstock-Kurzweil integral. We give conditions for the existence, continuity and differentiability of the Laplace transform. A Riemann-Lebesgue Lemma is given, and it is proved that the Laplace transform of a convolution is the pointwise product of Laplace transforms.

In this paper, we apply the Laplace decomposition method to obtain a series solutions of the Burgers-Huxley and Burgers-Fisher equations. The technique is based on the application of Laplace transform to nonlinear partial differential equations. The method does not need linearization, weak nonlinearity assumptions or perturbation theory and the nonlinear terms can be easily handled by using the...

We compute the asymptotic determinant of the discrete Laplacian on a simplyconnected rectilinear region in R2. Specifically, for each > 0 let H be the subgraph of Z2 whose vertices lie in a fixed rectilinear polygon U . Let N (H ) denote the number of vertices of H and B(H ) the number of vertices on the boundary (the outer face). Then the log of the determinant of the Laplacian on H has the fo...

In this work we focus on approximations of continuous harmonic functions by discrete harmonic functions based on the discrete Laplacian in a triangulation of a point set. We show how the choice of edge weights based on generalized barycentric coordinates influences the approximation quality of discrete harmonic functions. Furthermore, we consider a varying point set to demonstrate that generali...

We prove an analogue of a classical asymptotic stability result of standing waves of the Schrödinger equation originating in work by Soffer and Weinstein. Specifically, our result is a transposition on the lattice Z of a result by Mizumachi [M1] and it involves a discrete Schrödinger operator H = −∆+q. The decay rates on the potential are less stringent than in [M1], since we require q ∈ l1,τ w...

There are a lot of researches on the spectrum of the discrete Laplacian on an infinite graph in various areas. One of main topics among them is to characterize the spectral structure in terms of a certain geometric property of the graph. We focus on the possibility of the absence of eigenvalues and give a criterion for this in terms of combinatorial property of a graph. A graph G is a connected...

We introduce the Laplace transform for an arbitrary time scale. Two particular choices of time scales, namely the reals and the integers, yield the concepts of the classical Laplace transform and of the classical Z-transform. Other choices of time scales yield new concepts of our Laplace transform, which can be applied to find solutions of higher order linear dynamic equations with constant coe...