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A numerical explicit method to evaluates transient solutions of linear partial differential non-homogeneous equation with constant coefficients is proposed.
Consider a non-linear operator equation $x - K(x) = f$, where $f$ is a given function and $K$ is a Urysohn integral operator with Green's function type kernel defined on $L^\infty [0, 1]$. We apply approximation methods based on…
We consider an approximate solution for the one-dimensional semilinear singularly-perturbed boundary value problem, using the previously obtained numerical values of the boundary value problem in the mesh points and the representation of…
We study semi-martingale obliquely reflected Brownian motion with drift in the first quadrant of the plane in the transient case. Our main result determines a general explicit integral expression for the moment generating function of…
We developed the formal connection of the field theoretical Bethe-Salpeter equation including the ladder approximation with its representation on the light-front for a bosonic model. We use the light-front Green's function for the…
In this article we use linear algebra to improve the computational time for the obtaining of Green's functions of linear differential equations with reflection (DER). This is achieved by decomposing both the `reduced' equation (the ODE…
Starting with the Green's functions found for normal diffusion, we construct exact time-dependent Green's functions for subdiffusive equation (with fractional time derivatives), with the boundary conditions involving a linear combination of…
This report provides Green's functions (classical propagators) of gravitational fields appearing in general relativity. The existence of Green's function of the wave equation in curved space with an indefinite metric is ensured owing to the…
In this paper we will show several properties of the Green's functions related to various boundary value problems of arbitrary even order. In particular, we will write the expression of the Green's functions related to the general…
Green's functions characterize the fundamental solutions of partial differential equations; they are essential for tasks ranging from shape analysis to physical simulation, yet they remain computationally prohibitive to evaluate on…
The inhomogenous time-fractional telegraph equation with Caputo derevatives with constant coefficients is considered. For considered equation the general representation of regular solution in rectangular domain is obtained, and the…
Recently, general point interactions in one dimension has been used to model a large number of different phenomena in quantum mechanics. Such potentials, however, requires some sort of regularization to lead to meaningful results. The usual…
The integral equation method is widely used in numerical simulations of 2D/3D acoustic and electromagnetic scattering problems, which needs a large number of values of the Green's functions. A significant topic is the scattering problems in…
The well-known Green's function method has been recently generalized to nonlinear second order differential equations. In this paper we study possibilities of exact Green's function solutions of nonlinear differential equations of higher…
Through this article we will use a notation \begin{equation}\label{alfaLap} T_{\alpha}u(x)=(1-|x|^2)\Delta u(x)+2 \alpha \langle x,\nabla u(x)\rangle + (n-2-\alpha) \alpha u(x). \end{equation} Here, $|x|<1$ and $\alpha>-1$. Also, for…
Gauge invariant quark two-point Green's functions defined with path-ordered gluon field phase factors along skew-polygonal lines joining the quark to the antiquark are considered. Functional relations between Green's functions with…
Based on a canonical approach and functional-integration techniques, a series expansion of Green's function of a scalar field, in the presence of a medium, is obtained. A series expansion for Lifshitz-energy, in finite-temperature, in terms…
I review the application of self-consistent Green's functions methods to study the properties of infinite nuclear systems. Improvements over the last decade, including the consistent treatment of three-nucleon forces and the development of…
In present paper we suggest exact solution of the Poisson problem which appears in frequently addressed applications regarding calculation of the gravitational potential of spiral galaxies. We suggest an analytical solution for the problem…
A stochastic method is described for estimating Green's functions (GF's), appropriate to linear advection-diffusion-reaction transport problems, evolving in arbitrary geometries. By allowing straightforward construction of approximate,…