The method of the fundamental solutions (MFS) is used to construct an approximate solution for a partial differential equation in bounded domain. It demonstrated by combining shifted points outside domain and determining coefficients linear sum satisfy boundary condition on finite boundary. In this paper, existence MFS Neumann problems modified Helmholtz disk domains rigorously demonstrated. We...

Within a light-cone QCD formalism based on the Green function technique incorporating color transparency and coherence length effects we study nuclear shadowing in deep-inelastic scattering at moderately small Bjorken xBj . Calculations performed so far were based only on approximations leading to an analytical harmonic oscillatory form of the Green function. We present for the first time an ex...

a simple new closed form of the green function for axisymmetric magnetostatic problemsis found analytically in cylindrical coordinates. the result is verified by applying several examples.

For the Laplacian ∆ defined on a p.c.f. self-similar fractal, we give an explicit formula for the resolvent kernel of the Laplacian with Dirichlet boundary conditions, and also with Neumann boundary conditions. That is, we construct a symmetric function G(λ) which solves (λI − ∆)−1 f (x) = ∫ G(λ)(x, y) f (y) dμ(y). The method is similar to Kigami’s construction of the Green kernel in [Kig01, §3...

The newly developed iterative method based on Green function defined by quadratures along a single trajectory is combined with the variational method to solve the ground state quantum wave function for central potentials. As an example , the method is applied to discuss the ground state solution of Yukawa potential, using Hulthen solution as the trial function.

Continuous optimization, data assimilation, determining model sensitivity, uncertainty quantification, and a posteriori estimation of computational error are fundamentally important problems in mathematical modeling of the physical world. There has been some substantial progress on solving these problems in recent years, and some of these solution techniques are entering mainstream computationa...

In this article, we give an integral representation of the resolvent kernel on H-type groups, then derive Kaplan's fundamental solution groups. Also obtain Green for fractional powers its sub-Laplacian.

Meshless methods based on the local Petrov-Galerkin approach are proposed for solution of steady and transient heat conduction problem in a continuously nonhomogeneous anisotropic medium. Fundamental solution of the governing partial differential equations and the Heaviside step function are used as the test functions in the local weak form. It is leading to derive local boundary integral equat...

we describe how to obtain electronic transport properties of disordered graphene, including the tight binding model and nearest neighbor hopping. we present a new method for computing, electronic transport wave function and greens function of the disordered graphene. in this method, based on the small rectangular approximation, break up the potential barriers in to small parts. then using the f...

background: alzheimer’s disease (ad) is the most prevalent degenerative disorder of the brain among elderly individuals. many studies indicate that oxidative stress is an important pathogenic factor which involves oxidizing macromolecules such as dna, lipids, and proteins in ad. green tea is a rich source of antioxidant compounds that can remove radical oxygen species. the purpose of this study...