Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2608.29932

Advancements in Spectral Collocation Methods for High-Order Eigenvalue Problems

Sameh Gana
View original source ↗Read source document ↗Export metadata ↓

Abstract

This paper focuses on computing spectral solutions for high-order eigenvalue problems using an efficient discretization method based on Chebfun spectral discretization algorithms and domain truncation. We solve several numerical eigenvalue problems, demonstrating both the accuracy and computational efficiency of the proposed approach.

Explore related subjects

math.NAcs.NA

Keep this discovery

BibTeXRIS

Sameh Gana. 2026-08-30. Advancements in Spectral Collocation Methods for High-Order Eigenvalue Problems. https://arxiv.org/abs/2608.29932

Cite the original work for its findings. Save a collection to share your selection of sources.

Discover connections

cs.NA subjectmath.NA subject

Connections use source metadata and explicit phrase matches, not verified experimental comparisons.

KEEP EXPLORING

Related papers

arXiv2026

Numerical experiments on the Hardy conjecture for the Gauss circle problem

The classical unsolved Gauss circle problem concerns estimating the error between the number of lattice points inside a circle and the area of the circle as its radius tends to infinity. About a century ago, Hardy proposed a conjecture concerning this problem. In this paper, we attempt to provide numerical evidence in support of the Hardy conjecture through large-scale numerical computations.

math.NT↗
arXiv2021

$L^p$-Convergence Rate of Backward Euler Schemes for Monotone SDEs

We give a unified method to derive the strong convergence rate of the backward Euler scheme for monotone SDEs in $L^p(Ω)$-norm, with general $p \ge 4$. The results are applied to the backward Euler scheme of SODEs with polynomial growth coefficients. We also generalize the argument to the Galerkin-based backward Euler scheme of SPDEs with polynomial growth coefficients driven by multiplicative trace-class noise.

math.NA↗
arXiv2026

An existence result of a functional integral equation via Darbo type theorem and an iterative algorithm to solve it

In our study, Darbo's fixed point theorem and the coupled fixed point theorem have been extended. The two theorems were generalized using $C-class$ mapping. Using the Darbo type theorem, we gave an existence result for a functional integral equation along with an appropriate illustration. In addition, we explored the numerical solution of a given functional integral problem using modified homotopy perturbation.

math.FA↗