Efficient Spectral-Galerkin Method II. Direct Solvers of Second- and Fourth-Order Equations Using Chebyshev Polynomials

نویسندگان

چکیده

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Efficient Spectral-Galerkin Method II. Direct Solvers of Second- and Fourth-Order Equations Using Chebyshev Polynomials

Efficient direct solvers based on the Chebyshev-Galerkin methods for second and fourth order equations are presented. They are based on appropriate base functions for the Galerkin formulation which lead to discrete systems with special structured matrices which can be efficiently inverted. Numerical results indicate that the direct solvers presented in this paper are significantly more accurate...

متن کامل

Efficient Spectral-Galerkin Method I. Direct Solvers of Second- and Fourth-Order Equations Using Legendre Polynomials

We present some efficient algorithms based on the Legendre-Galerkin approximations for the direct solution of the second and fourth order elliptic equations. The key to the efficiency of our algorithms is to construct appropriate base functions, which lead to systems with sparse matrices for the discrete variational formulations. The complexities of the algorithms are a small multiple of N oper...

متن کامل

Efficient spectral-Galerkin methods for systems of coupled second-order equations and their applications

We construct in this paper two efficient spectral-Galerkin algorithms for solving systems of n coupled second-order equations. The computational complexity of these algorithms is essentially n times the cost of solving one second-order equation. We present numerical results which illustrate the accuracy and flexibility of these algorithms, as well as several interesting and challenging applicat...

متن کامل

Application of Chebyshev Polynomials for Solving Abel's Integral Equations of the First and Second Kind

In this paper, a numerical implementation of an expansion method is developed for solving Abel's integral equations of the first and second kind. The solution of such equations may demonstrate a singular behaviour in the neighbourhood of the initial point of the interval ofintegration. The suggested method is based on the use of Taylor series expansion to overcome the singularity which le...

متن کامل

A spectral method based on Hahn polynomials for solving weakly singular fractional order integro-differential equations

In this paper, we consider the discrete Hahn polynomials and investigate their application for numerical solutions of the fractional order integro-differential equations with weakly singular kernel .This paper presented the operational matrix of the fractional integration of Hahn polynomials for the first time. The main advantage of approximating a continuous function by Hahn polynomials is tha...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: SIAM Journal on Scientific Computing

سال: 1995

ISSN: 1064-8275,1095-7197

DOI: 10.1137/0916006