Iterated discrete polynomially based Galerkin methods

• Published in: Applied mathematics and computation Vol. 146; no. 1; pp. 153 - 165
• Main Authors: Kulkarni, Rekha P., Gnaneshwar, N.
• Format: Journal Article
• Language: English
• Published: New York, NY Elsevier Inc 30-12-2003; Elsevier
• Subjects: Convergence rates; Exact sciences and technology; Integral equations; Integral equations, integral transforms; Iterated discrete Galerkin; Mathematical analysis; Mathematics; Numerical analysis; Numerical analysis. Scientific computation; Polynomially based; Sciences and techniques of general use; Spectral approximation; Iterated discrete Galerkin; Spectral approximation; Integral equations; Convergence rates; Polynomially based; Integral operator; Error estimation; Polynomial approximation; Singular equation; Iterative method; Discretization method; Fredholm equation; Spectrum; Applied mathematics; Convergence rate; Integral equation; Galerkin method; Eigenvalue problem; Combustion efficiency
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/S0096-3003(02)00533-7

Golberg and Bowman [Appl. Math. Comput. 96 (1998) 237] have studied polynomially based discrete Galerkin method for Fredholm and Singular integral equations. In this paper we consider polynomially based iterated discrete Galerkin method for solution of operator equations and for eigenvalue problem associated with an integral operator with a smooth kernel. We show that the error in the infinity norm, both for approximation of operator equation and of spectral subspace, is of the order of
n
−
r
, where
n is the degree of the polynomial approximation and
r is the smoothness of the kernel. Thus the iterated discrete Galerkin solution improves upon the discrete Galerkin solution, which was shown to be of order
n
−
r+1
by Golberg and Bowman [Appl. Math. Comput. 96 (1998) 237]. We also give a shorter proof of the result by Golberg and Bowman which states that the error in 2-norm in discrete Galerkin method is of the order of
n
−
r
.