Efficient Chebyshev–Petrov–Galerkin Method for Solving Second ...

A new efficient Chebyshev–Petrov–Galerkin (CPG) direct solver is presented for the second order elliptic problems in square domain where the ...

A new efficient Chebyshev–Petrov–Galerkin (CPG) direct solver is presented for the second order elliptic problems in square domain where the Dirichlet and ...

Petrov---Galerkin Method for Solving Second-Order Equations

A new efficient Chebyshev---Petrov---Galerkin (CPG) direct solver is presented for the second order elliptic problems in square domain.

Efficient and accurate Chebyshev dual-Petrov-Galerkin methods for ...

of our greatest interests due to the FFT for Chebyshev polynomials. Standard Chebyshev spectral methods have been extensively investigated for solving second-.

Efficient Spectral-Galerkin Method II. Direct Solvers of Second

Efficient direct solvers based on the Chebyshev–Galerkin methods for second- and fourth-order equations are presented.

[PDF] Efficient Spectral-Galerkin Method II. Direct Solvers of Second

Numerical results indicate that the direct solvers presented in this paper are significantly more accurate and efficient than those based on the ...

Efficient Spectral-Galerkin Method II. Direct Solvers of Second and ...

Although using Legendre polynomials offers many advantage over using Chebyshev polynomials, such as symmetricity and sparseness of the matrices for the discrete ...

The a posteriori error estimates of Chebyshev–Petrov–Galerkin ...

Specially, the author in [3] employed the k th derivatives of Chebyshev polynomials to present an efficient CPG spectral method for solving second-order ...

Improving Petrov–Galerkin elements via Chebyshev polynomials ...

Two types of univariate Petrov–Galerkin elements using piecewise polynomials are described by Chen and Xu (1998) and four lemmas are proved ...

Mortensen, Mikael A generic and strictly banded spectral Petrov ...

[12] Elbarbary, E. M. E., Efficient Chebyshev-Petrov-Galerkin method for solving second-order equations, J. Sci. Comput., 34. (2008), pp. 113-126, doi ...

Efficient Spectral-Galerkin Method I. Direct Solvers of Second

This paper presents some efficient algorithms based on the Legendre–Galerkin approximations for the direct solution of the second- and fourth-order elliptic ...

Chebyshev Galerkin method for integro-diﬀerential equations of the ...

In this paper, we propose an efficient implementation of the Chebyshev Galerkin method for first order Volterra and Fredholm ...

Efficient Legendre dual-Petrov-Galerkin methods for odd-order ...

Recently, Ma and Sun [12,13] developed an efficient Legendre-Petrov-Galerkin and Chebyshev collocation method for the third-order differential equations and ...

Solving real-life BVPs via the second derivative Chebyshev pseudo ...

Then, the operational matrix for the derivative was established by using SDCHPs. The established matrix via mixing between two spectral methods, collocation and ...

Efficient and Accurate Chebyshev Dual-Petrov-Galerkin Methods for ...

Efficient and accurate Chebyshev dual-Petrov-Galerkin methods for solving first-order equation, third-order equation, third-order KdV equation and fifth ...

A generic sparse spectral Petrov-Galerkin method - UiO - DUO

[12] E. M. E. Elbarbary, Efficient Chebyshev–Petrov–Galerkin Method for Solving Second-Order. 747. Equations, Journal of Scientific Computing, 34 (2008), pp ...

Legendre-Petrov-Galerkin Chebyshev spectral collocation method ...

We propose a Legendre-Petrov-Galerkin Chebyshev spectral collocation method for initial value problems (IVPs) of second-order nonlinear ordinary ...

Chebyshev expansion method for solving second and fourth-order ...

Elbarbary E(2008)Efficient Chebyshev---Petrov---Galerkin Method for Solving Second-Order EquationsJournal of Scientific Computing10.1007/s10915-007-9161-934 ...

An efficient spectral-Galerkin method for solving two-dimensional ...

Boyd JP (2000) Chebyshev and Fourier spectral methods, 2nd edn. · Dehghan M (2004) Numerical solution of the three-dimensional advection–diffusion equation.

Two Legendre-Dual-Petrov-Galerkin Algorithms for Solving the ...

Two numerical algorithms based on dual-Petrov-Galerkin method are developed for solving the integrated forms of high odd-order boundary value problems ...