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 …

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 …

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 …

This paper introduces general methodologies for constructing closed-form solutions to linear
constant-coefficient partial differential equations (PDEs) with polynomial right-hand sides in …

This paper presents the particular solutions for the polyharmonic and the products of
Helmholtz partial differential operators with polyharmonic splines and monomials right-hand …

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 …

In this paper we develop analytical particular solutions for the polyharmonic and the
products of Helmholtz-type partial differential operators with Chebyshev polynomials at …

This paper introduces general methodologies for constructing closed-form solutions to
several important partial differential equations (PDEs) with polynomial right-hand sides in …

In this paper, we extended the method of approximate particular solutions (MAPS) using
trigonometric basis functions to solve two-dimensional elliptic partial differential equations …

In this paper we derive analytical particular solutions for the axisymmetric polyharmonic and
poly-Helmholtz partial differential operators using Chebyshev polynomials as basis …