Work

Projection-based approximations for eigenvalue problems of Fredholm integral operators with Green's kernels

Year: 2026

Type: preprint

Abstract: We consider the eigenvalue problem $K x = λx$. Our analysis focuses on the convergence rates of eigenvalue and spectral subspace approximations for compact linear integral operator $K$ with Green's kernels. By employing orthogonal and interpolatory projections at $2r+1$ collocation points (which are not necessarily Gauss points) onto an approximating space of piecewise even degree polynomials, we establish the superconvergence of eigenfunctions under iteration. The modified projection methods achieve a faster convergence rates compared to classical projection methods. The enhancement in convergence rate is verified by numerical examples.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2602.16191

Authors: Shukla, Shashank K., Rakshit, Gobinda, Rane, Akshay S.

Institutions: Rajiv Gandhi Institute of Petroleum Technology, Institute of Chemical Technology

Topic: Mathematical functions and polynomials

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7130542129

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