In this work, we conduct a comparative study among the combine Laplace transform and modied Adomian decomposition method (LMADM) and two traditional methods for an analytic and approximate treatment of special type of nonlinear Volterra integro-differential equations of the second kind. The nonlinear part of integro-differential is approximated by Adomian polynomials, and the equation is reduce...

The networks of this – primarily (but not exclusively) expository compendium are strongly connected, finite directed graphs X, where each oriented edge (x,y) is equipped with a positive weight (conductance) a(x,y). We assuming symmetry function, and in general we do require that along (x,y), also (y,x) an edge. weights give rise to difference operator, the normalised version which consider as o...

It is well known that the Green function of the standard discrete Laplacian on l2(Zd), ∆stψ(n) = (2d) −1 ∑ |n−m|=1 ψ(m), exhibits a pathological behavior in dimension d ≥ 3. In particular, the estimate 〈δ0|(∆st − E − i0)δn〉 = O(|n|− d−1 2 ) fails for 0 < |E| < 1 − 2/d. This fact complicates the study of the scattering theory of discrete Schrödinger operators. Molchanov and Vainberg suggested th...

This paper is concerned with the asymptotic behavior of the trav-eling wave fronts in Lotka-Volterra competition system. By Laplacian transform, we prove that the traveling wave fronts of the system grow exponentially when the traveling coordinate tends to negative infinity.

Fundamental solutions of dynamic poroelasticity and generalized thermoelasticity are derived in the Laplace transform domain. For poroelasticity, these solutions define the solid displacement field and the fluid pressure in fluid-saturated media due to a point force in the solid and an injection of fluid in the pores. In addition, approximate fundamental solutions for short times are derived by...

Reduced Differental Transform Method (RDTM), which is one 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 results demonstrated that RDTM is a powerful tool for solving nonlinear part...

In this paper, Adomian decomposition method (ADM) and Laplace decomposition method (LDM) used to obtain series solutions of Burgers-Huxley and Burgers-Fisher Equations. In ADM the algorithm is illustrated by studying an initial value problem and LDM is based on the application of Laplace transform to nonlinear partial differential equations. In ADM only few terms of the expansion are required t...

Two parametric models for income and financial return distributions are presented. There are the four-parameter normal Laplace (NL) and the five-parameter generalized normal Laplace (GNL) distributions. Their properties are discussed; furthermore, estimation of the parameters by the method of moments and maximum likelihood is presented. The performances of fitting the two models to nine empiric...

The Laplace-Beltrami operator for graphs has been been widely used in many machine learning issues, such as spectral clustering and transductive inference. Functions on the nodes of a graph with vanishing Laplacian are called harmonic functions. In differential geometry, the Laplace-de Rham operator generalizes the Laplace-Beltrami operator. It is a differential operator on the exterior algebra...