A fast and well-conditioned spectral method
A spectral method is developed for the direct solution of linear ordinary differential equations
with variable coefficients and general boundary conditions. The method leads to matrices …
with variable coefficients and general boundary conditions. The method leads to matrices …
Tensor calculus in spherical coordinates using Jacobi polynomials. Part-I: mathematical analysis and derivations
This paper presents a method for accurate and efficient computations on scalar, vector and
tensor fields in three-dimensional spherical polar coordinates. The method uses spin …
tensor fields in three-dimensional spherical polar coordinates. The method uses spin …
New algorithms for solving high even-order differential equations using third and fourth Chebyshev–Galerkin methods
This paper is concerned with spectral Galerkin algorithms for solving high even-order two
point boundary value problems in one dimension subject to homogeneous and …
point boundary value problems in one dimension subject to homogeneous and …
Legendre-Chebyshev spectral collocation method for two-dimensional nonlinear reaction-diffusion equation with Riesz space-fractional
A high accurate spectral algorithm for two-dimensional nonlinear reaction-diffusion equation
with Riesz space-fractional (RF-TNRDEs) is consider. We propose a shifted Legendre …
with Riesz space-fractional (RF-TNRDEs) is consider. We propose a shifted Legendre …
[PDF][PDF] Ultraspherical wavelets method for solving Lane–Emden type equations
In this paper, a new shifted ultraspherical wavelets operational matrix of derivatives is
introduced. The two wavelets operational matrices, namely Legendre and first kind …
introduced. The two wavelets operational matrices, namely Legendre and first kind …
Tensor calculus in polar coordinates using Jacobi polynomials
Spectral methods are an efficient way to solve partial differential equations on domains
possessing certain symmetries. The utility of a method depends strongly on the choice of …
possessing certain symmetries. The utility of a method depends strongly on the choice of …
On the coefficients of differentiated expansions and derivatives of Chebyshev polynomials of the third and fourth kinds
Two new analytical formulae expressing explicitly the derivatives of Chebyshev polynomials
of the third and fourth kinds of any degree and of any order in terms of Chebyshev …
of the third and fourth kinds of any degree and of any order in terms of Chebyshev …
Efficient spectral-Petrov-Galerkin methods for third-and fifth-order differential equations using general parameters generalized Jacobi polynomials
Two new families of general parameters generalized Jacobi polynomials are introduced.
Some efficient and accurate algorithms based on these families are developed and …
Some efficient and accurate algorithms based on these families are developed and …
A novel operational matrix method based on shifted Legendre polynomials for solving second-order boundary value problems involving singular, singularly perturbed …
In this article, a new operational matrix method based on shifted Legendre polynomials is
presented and analyzed for obtaining numerical spectral solutions of linear and nonlinear …
presented and analyzed for obtaining numerical spectral solutions of linear and nonlinear …
[HTML][HTML] Solving boundary value problems, integral, and integro-differential equations using Gegenbauer integration matrices
We introduce a hybrid Gegenbauer (ultraspherical) integration method (HGIM) for solving
boundary value problems (BVPs), integral and integro-differential equations. The proposed …
boundary value problems (BVPs), integral and integro-differential equations. The proposed …