Related papers: Numerical Solution of the Modified Bessel Equation
Green's function plays a significant role in both theoretical analysis and numerical computing of partial differential equations (PDEs). However, in most cases, Green's function is difficult to compute. The troubles arise in the following…
This paper presents a novel framework for enclosing solutions of Poisson's equation based on generalized sub- and super-solutions constructed using fundamental solutions. The conventional definition of sub- and super-solutions based on…
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…
Using a deformed calculus based on the Dunkl operator, two new deformations of Bessel functions are proposed. Some properties i.e. generating function, differential-difference equation, recursive relations, Poisson formula... are also given…
We revisit the Fourier transform of a Hankel function, of considerable importance in the theory of knife edge diffraction. Our approach is based directly upon the underlying Bessel equation, which admits manipulation into an alternate…
We present a numerical method for solving the Poisson equation on a nested grid. The nested grid consists of uniform grids having different grid spacing and is designed to cover the space closer to the center with a finer grid. Thus our…
We present a method of solving partial differential equations on the $n$-dimensional unit sphere using methods based on the continuous wavelet transform derived from approximate identities. We give an explicit analytical solution to the…
A new method is presented to obtain a closed form of the generalized Green function to the Poisson and the Helmholtz equations on the $n$-dimensional unit sphere.
In this work we present a numerical method to solve the set of Dyson-like equations arising the context of non-equilibrium Green's functions. The technique is based on the self-consistent solution of the Dyson equations for the interacting…
This paper studies an efficient numerical method for solving modified Poisson-Boltzmann (MPB) equations with the self Green's function as a state equation to describe electrostatic correlations in ionic systems. Previously, the most…
This paper is a revised version of the original paper of same title--published in Applied Mathematics Letters 89--containing some corrections and clarifications to the original text. We derive non-singular Green's functions for the…
The modified Poisson-Boltzmann (MPB) equations are often used to describe equilibrium particle distribution of ionic systems. In this paper, we propose a fast algorithm to solve MPB equations with the self Green's function as the self…
A new approximation method for inverting the Poisson's equation is presented for a continuously distributed and finite-sized source in an unbound domain. The advantage of this image multipole method arises from its ability to place the…
A new method is presented for solving Poisson's equation inside an open-ended rectangular pipe. The method uses Fast Fourier Transforms (FFTs) to perform mixed convolutions and correlations of the charge density with the Green function.…
In this paper, the Green's function and decomposition technique is proposed for solving the coupled Lane-Emden equations. This approach depends on constructing Green's function before establishing the recursive scheme for the series…
We derive formulas for the matrix elements of the lattice Green function for the discrete Poisson equation on an infinite square lattice. The partial difference equation for the matrix elements is solved by reducing it to a series of first…
In this paper, we study Dirichlet problems of fractional Laplace (Poisson) equations on a general bounded domain in $\mathbb{R}^n$. Green's functions and Poisson kernels are important tools needed in our study. We first establish the…
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…
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…
In geophysical fluid dynamics, the screened Poisson equation appears in the shallow-water, quasi geostrophic equations. Recently, many attempts have been made to solve those equations on the sphere using different numerical methods. These…