Numerical simulation of 3D nonlinear Schrödinger equations by using the localized method of approximate particular solutions
Sign Up to like & getrecommendations! Published in 2017 at "Engineering Analysis With Boundary Elements"
DOI: 10.1016/j.enganabound.2017.02.002
Abstract: Abstract In this paper, we describe a novel sparse meshless approach to the simulations of three-dimensional time-dependent nonlinear Schrodinger equations. Our procedure is implemented in two successive steps. In the first step, the implicit-Euler scheme… read more here.
Keywords: approximate particular; method approximate; method; particular solutions ... See more keywords
The closed-form particular solutions for the Laplace operator using oscillatory radial basis functions in 2D
Sign Up to like & getrecommendations! Published in 2018 at "Engineering Analysis with Boundary Elements"
DOI: 10.1016/j.enganabound.2018.09.002
Abstract: Abstract The closed-form particular solutions of the radial basis functions (RBFs) are essential for the implementation of several numerical methods to solve various partial differential equations (PDEs). Recently, a new class of oscillatory RBFs has… read more here.
Keywords: radial basis; basis functions; particular solutions; closed form ... See more keywords
Comparisons of method of fundamental solutions, method of particular solutions and the MFS-QR; stability analysis
Sign Up to like & getrecommendations! Published in 2021 at "Engineering Analysis With Boundary Elements"
DOI: 10.1016/j.enganabound.2020.11.017
Abstract: Abstract The goals of this paper are twofold: selection of pseudo-boundaries for sources nodes in the method of fundamental solutions (MFS), and comparisons of the MFS, the method of particular solutions (MPS) and the MFS-QR… read more here.
Keywords: solutions mfs; mps mfs; analysis; particular solutions ... See more keywords
Method of Particular Solutions for Second-Order Differential Equation with Variable Coefficients via Orthogonal Polynomials
Sign Up to like & getrecommendations! Published in 2023 at "Journal of Function Spaces"
DOI: 10.1155/2023/9748605
Abstract: In this paper, with classic Legendre polynomials, a method of particular solutions (MPS, for short) is proposed to solve a kind of second-order differential equations with a variable coefficient on a unit interval. The particular… read more here.
Keywords: order differential; polynomials method; particular solutions; method particular ... See more keywords