Localized Chebyshev collocation method for solving elliptic partial differential equations in arbitrary 2D domains
In this paper, a novel collocation method is presented for the efficient and accurate
evaluation of the two-dimensional elliptic partial differential equation. In the new method, the …
evaluation of the two-dimensional elliptic partial differential equation. In the new method, the …
[HTML][HTML] Numerical solutions of elliptic partial differential equations using Chebyshev polynomials
We present a simple and effective Chebyshev polynomial scheme (CPS) combined with the
method of fundamental solutions (MFS) and the equilibrated collocation Trefftz method for …
method of fundamental solutions (MFS) and the equilibrated collocation Trefftz method for …
Matrix decomposition algorithms for elliptic boundary value problems: a survey
B Bialecki, G Fairweather, A Karageorghis - Numerical algorithms, 2011 - Springer
We provide an overview of matrix decomposition algorithms (MDAs) for the solution of
systems of linear equations arising when various discretization techniques are applied in the …
systems of linear equations arising when various discretization techniques are applied in the …
Construction of polynomial particular solutions of linear constant-coefficient partial differential equations
TG Anderson, M Bonnet, LM Faria… - … & Mathematics with …, 2024 - Elsevier
This paper introduces general methodologies for constructing closed-form solutions to linear
constant-coefficient partial differential equations (PDEs) with polynomial right-hand sides in …
constant-coefficient partial differential equations (PDEs) with polynomial right-hand sides in …
Particular solutions of splines and monomials for polyharmonic and products of Helmholtz operators
This paper presents the particular solutions for the polyharmonic and the products of
Helmholtz partial differential operators with polyharmonic splines and monomials right-hand …
Helmholtz partial differential operators with polyharmonic splines and monomials right-hand …
[HTML][HTML] The method of particular solutions using trigonometric basis functions
In this paper, the method of particular solutions (MPS) using trigonometric functions as the
basis functions is proposed to solve two-dimensional elliptic partial differential equations …
basis functions is proposed to solve two-dimensional elliptic partial differential equations …
[PDF][PDF] Particular solutions of Chebyshev polynomials for polyharmonic and poly-Helmholtz equations
CC Tsai - CMES: Computer Modeling in Engineering & Sciences, 2008 - Citeseer
In this paper we develop analytical particular solutions for the polyharmonic and the
products of Helmholtz-type partial differential operators with Chebyshev polynomials at …
products of Helmholtz-type partial differential operators with Chebyshev polynomials at …
On particular solutions of linear partial differential equations with polynomial right-hand-sides
TG Anderson, M Bonnet, LM Faria… - arXiv preprint arXiv …, 2023 - arxiv.org
This paper introduces general methodologies for constructing closed-form solutions to
several important partial differential equations (PDEs) with polynomial right-hand sides in …
several important partial differential equations (PDEs) with polynomial right-hand sides in …
The MAPS based on trigonometric basis functions for solving elliptic partial differential equations with variable coefficients and Cauchy–Navier equations
In this paper, we extended the method of approximate particular solutions (MAPS) using
trigonometric basis functions to solve two-dimensional elliptic partial differential equations …
trigonometric basis functions to solve two-dimensional elliptic partial differential equations …
The method of particular solutions for solving axisymmetric polyharmonic and poly-Helmholtz equations
In this paper we derive analytical particular solutions for the axisymmetric polyharmonic and
poly-Helmholtz partial differential operators using Chebyshev polynomials as basis …
poly-Helmholtz partial differential operators using Chebyshev polynomials as basis …