TITLE

# Legendre spectral-collocation method for Volterra integral equations with non-vanishing delay

AUTHOR(S)
Gu, Zhendong; Chen, Yanping
PUB. DATE
March 2014
SOURCE
Calcolo;Mar2014, Vol. 51 Issue 1, p151
SOURCE TYPE
DOC. TYPE
Article
ABSTRACT
The main purpose of this paper is to propose the Legendre spectral-collocation method to solve the Volterra integral equations of the second kind with non-vanishing delay. We divide the definition domain into several subintervals according to the primary discontinuous points associated with the delay. In each subinterval, where the solution is smooth enough, we can apply Legendre spectral-collocation method to approximate the solution. The provided convergence analysis shows that the numerical errors decay exponentially. Numerical examples are presented to confirm this theoretical predict.
ACCESSION #
94725237

## Related Articles

• Homotopy approximation technique for solving nonlinear Volterra-Fredholm integral equations of the first kind. Behzadi, Sadigh // International Journal of Industrial Mathematics;2014, Vol. 6 Issue 4, p315

In this paper, a nonlinear Volterra-Fredholm integral equation of the first kind is solved by using the homotopy analysis method (HAM). In this case, the first kind integral equation can be reduced to the second kind integral equation which can be solved by HAM. The approximate solution of this...

• Numerical Scheme for Fredholm Integral Equations Optimal Control Problems via Bernstein Polynomials. Sanchooli, Mahmood; Fard, Omid Solaymani // Australian Journal of Basic & Applied Sciences;2010, Vol. 4 Issue 11, p5675

In this paper, we present a novel iterative method to approximate the solution to a class of optimal control problems governed by Fredholm integral equations. We are willing to construct a direct scheme based on the Bernstein polynomials and parameterization. The convergence of the method is...

• Approximation in statistical sense by n-multiple sequences of fuzzy positive linear operators. Demirci, Kamil; Karakuş, Sevda // Studia Universitatis Babes-Bolyai, Mathematica;Sep2012, Vol. 57 Issue 3, p387

Our primary interest in the present paper is to prove a Korovkin-type approximation theorem for n-multiple sequences of fuzzy positive linear operators via statistical convergence. Also, we display an example such that our method of convergence is stronger than the usual convergence.

• Numerical approximation of elliptic control problems with finitely many pointwise constraints. Casas, Eduardo; Mateos, Mariano // Computational Optimization & Applications;Apr2012, Vol. 51 Issue 3, p1319

We study the numerical approximation of elliptic control problems with finitely many pointwise state constraints and control bounds. Results for the continuous problem are collected and a complete study of the discrete problems is carried out, including, existence of solutions, optimality...

• A MIXED FINITE ELEMENT METHOD FOR THE CONTACT PROBLEM IN ELASTICITY. Dong-ying Hua; Lie-heng Wang // Journal of Computational Mathematics;Jul2005, Vol. 23 Issue 4, p441

Based on the analysis of  and , we present the mixed finite element approximation of the variational inequality resulting from the contact problem in elasticity. The convergence rate of the stress and displacement field are both improved from O(hÂ¾) to quasi-optimal O(h|logh|Â¼). If...

• RESOURCE CONSUMPTION OPTIMAL AND QUASI-OPTIMAL CONTROLS FOR DYNAMIC SYSTEMS. ALEKSANDROV, V. M. // Sibirskie Elektronnye Matematicheskie Izvestiia;2010, Vol. 7, p166

A numerical method of solving the problem on minimization of consumption resources for dynamic systems is proposed. The method is based on developing finite control translating a linear system in the fixed time from an initial state to a desired final state and allowing the structure of resource...

• Accelerating the convergence of higher-order coupled cluster methods. Matthews, Devin A.; Stanton, John F. // Journal of Chemical Physics;2015, Vol. 143 Issue 20, p1

The problem of the generally inferior convergence behavior of higher-order coupled cluster methods, such as CCSDT and CCSDTQ, compared to CCSD is analyzed in terms of MÃ¸ller-Plesset perturbation theory. A new structure for the CCSDT and CCSDTQ equations (and various approximations of these)...

• Coarse models for efficient space mapping optimisation of microwave structures. Koziel, S.; Bandler, J.W. // IET Microwaves, Antennas & Propagation;Apr2010, Vol. 4 Issue 4, p453

It follows from both theoretical results and practical observations that the coarse model is one of the most critical components of the space mapping optimisation process, affecting both the algorithm's ability of finding a high-quality design, and its computational complexity. A good coarse...

• A Lobatto interpolation grid over the triangle. BLYTH, M. G.; POZRIKIDIS, C. // IMA Journal of Applied Mathematics;Feb2006, Vol. 71 Issue 1, p153

A sequence of increasingly refined interpolation grids over the triangle is proposed, with the goal of achieving uniform convergence and ensuring high interpolation accuracy. The number of interpolation nodes, N, corresponds to a complete mth-order polynomial expansion with respect to the...

Share