Related papers: Wavelet based solutions to the Poisson and the Hel…
A solver for the Poisson equation for 1D, 2D and 3D regular grids is presented. The solver applies the convolution theorem in order to efficiently solve the Poisson equation in spectral space over a rectangular computational domain.…
A method is described to solve the Poisson problem for a three dimensional source distribution that is periodic into one direction. Perpendicular to the direction of periodicity a free space (or open) boundary is realized. In beam physics,…
The theory of orthogonal polynomials on the unit circle is developed for a general class of weights leading to systems of recurrence relations and derivatives of the polynomials and their associated functions, and to functional-difference…
We present an efficient method to solve the narrow capture and narrow escape problems for the sphere. The narrow capture problem models the equilibrium behavior of a Brownian particle in the exterior of a sphere whose surface is reflective,…
Capturing solution near the singular point of any nonlinear SBVPs is challenging because coefficients involved in the differential equation blow up near singularities. In this article, we aim to construct a general method based on…
We have constructed a sequence of solutions of the Helmholtz equation forming an orthogonal sequence on a given surface. Coefficients of these functions depend on an explicit algebraic formulae from the coefficient of the surface. Moreover,…
In this paper, we are concerned with $n$-dimensional spherical wavelets derived from the theory of approximate identities. For nonzonal bilinear wavelets introduced by Ebert \emph{et al.} in 2009 we prove isometry and Euclidean limit…
Multiresolution analyses based upon interpolets, interpolating scaling functions introduced by Deslauriers and Dubuc, are particularly well-suited to physical applications because they allow exact recovery of the multiresolution…
A collection of algorithms is described for numerically computing with smooth functions defined on the unit sphere. Functions are approximated to essentially machine precision by using a structure-preserving iterative variant of Gaussian…
We present a spectral method for solving elliptic equations which arise in general relativity, namely three-dimensional scalar Poisson equations, as well as generalized vectorial Poisson equations of the type $\Delta \vec{N} + \lambda…
In the frame of the traditional wavelet-Galerkin method based on the compactly supported wavelets, it is important to calculate the so-called connection coefficients that are some integrals whose integrands involve products of wavelets,…
In this series of eight papers we present the applications of methods from wavelet analysis to polynomial approximations for a number of accelerator physics problems. In this part we consider the applications of discrete wavelet analysis…
In the paper by means of Fourier transform method and similarity method we solve the Dirichlet problem for a multidimensional equation wich is a generalization of the Tricomi, Gellerstedt and Keldysh equations in the half-space, in which…
Reciprocal space methods for solving Poisson's equation for finite charge distributions are investigated. Improvements to previous proposals are presented, and their performance is compared in the context of a real-space density functional…
We introduce a two-phase approximation method designed to resolve singularities in three-dimensional harmonic Dirichlet problems. The approach utilizes the classical Green's function representation, decomposing the function into its…
In this paper, we investigate the abstract non-scalar Volterra difference equations. We employ the Poisson like transforms to connect the solutions of the abstract non-scalar Volterra integro-differential equations and the abstract…
An efficient algorithm for solving Poisson's equation in two and three spatial dimensions is discussed. The algorithm, which is described in detail, is based on the integral form of Poisson's equation and utilizes spherical coordinates and…
The multivariate analogue of Dalamber's equation in the space of generalized functions is considered. The method of generalized functions for the building of solutions of nonstationary boundary value problems for wave equations in spaces of…
In this paper, after a brief review of the general theory concerning regularized derivatives and integrals of a function with respect to another function, we provide a peculiar fractional generalization of the $(1+1)$-dimensional Dodson's…
In [18], fundamental solutions for the generalized bi-axially symmetric Helmholtz equation were constructed in $R_2^ + = \left\{ {\left( {x,y} \right):x > 0,y > 0} \right\}.$ They contain Kummer's confluent hypergeometric functions in three…