A new numerical method for a class of Volterra and Fredholm integral equations

Angelis, Paolo De; Marchis, Roberto De; Martire, Antonio Luciano

doi:10.1016/j.cam.2020.112944

Cited by 9 publications

(4 citation statements)

References 14 publications

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“…In Table 5, we have compared between the errors of present results for Example 4 corresponding to different values of collocation points N and those obtained by Maleknejad's method (MAL) reported in [29] and Mean Value eorem (MVT) reported in [25]. It can be seen that the present method converges rapidly compared to the Table 6 shows the maximum absolute errors of u(x) for Example 4 at different orders of approximation at selected nodes.…”

Section: Resultsmentioning

confidence: 91%

A New Numerical Technique for Solving Volterra Integral Equations Using Chebyshev Spectral Method

Khidir

2021

Mathematical Problems in Engineering

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In this work, we propose a new method for solving Volterra integral equations. The technique is based on the Chebyshev spectral collocation method. The application of the proposed method leads Volterra integral equation to a system of algebraic equations that are easy to solve. Some examples are presented and compared with some methods in the literature to illustrate the ability of this technique. The results demonstrate that the new method is more efficient, convergent, and accurate to the exact solution.

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Section: Resultsmentioning

confidence: 91%

A New Numerical Technique for Solving Volterra Integral Equations Using Chebyshev Spectral Method

Khidir

2021

Mathematical Problems in Engineering

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“…The exact solution is u(x) = 1 10 x 10 . The problem is already solved using cubic spline [35] and a method based on mean-value theorem [36]. We solved the problem using cubic spline approach.…”

Section: Convergence Analysis and Error Estimationmentioning

confidence: 99%

A novel super-convergent numerical method for solving nonlinear Volterra integral equations based on B-splines

Ghasemi,

Goligerdian,

Moradi

2023

Preprint

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‎We introduce and thoroughly examine a novel approach grounded in B-spline techniques to address the solution of second-kind nonlinear Volterra integral equations‎. ‎Our method revolves around the application of B-spline interpolation‎, ‎incorporating innovative end conditions‎, ‎and delving into the associated existence and error estimation aspects‎. ‎Notably‎, ‎we develop this technique separately for even and odd-degree splines‎, ‎leading to super-convergent approximations‎, ‎particularly significant when employing even-degree splines‎. ‎This paper extends its commitment to a comprehensive analysis‎, ‎delving deeply into the method's convergence characteristics and providing insightful error bounds‎. ‎To empirically validate our approach‎, ‎we present a series of numerical experiments‎. ‎These experiments underscore the method's efficacy and practicality‎, ‎showcasing numerical approximations that closely align with the anticipated theoretical outcomes‎. ‎Our proposed method thus emerges as a promising and robust tool for addressing the challenging realm of nonlinear Volterra integral equations‎, ‎bridging the gap between theoretical expectations and practical applications‎. 2010 Mathematics Subject Classifications: 45Dxx; 65R20; 41A15.

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“…Systems of Volterra integral equations with identically singular matrices in the principal part are called integral algebraic equations. Such equations and systems frequently arise in theoretical [7,9,14,25,29,35] and many applied problems especially in the fields of dynamic processes in chemical reactors [17], identification of memory kernels in heat conduction [32] viscoelastic materials [15], evolution of a chemical reaction within a small cell [16] and Kirchhoff's laws. The theory of IAEs appeared from early attempts by Gear in the 1990 that determined the difficulties of these equations.…”

Section: Introductionmentioning

confidence: 99%

A numerical solution of Volterra integral-algebraic equations using Bernstein polynomials

Enteghami-Orimi¹,

Babakhani²,

Hosainzadeh³

2021

MMN

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The principal aim of this paper is to serve the numerical solution for a linear integralalgebraic equation (IAE) by using Bernstein polynomials. Employing of Bernstein polynomials, the system of integral equations is approximated by the Gaussian quadrature formula with respect to the Legendre weight function. The proposed method reduces the system of integral equations to a system of algebraic equations that can be easily solved by any usual numerical method. Moreover, the convergence analysis of this algorithm will be shown by preparing some theorems. Several examples are included to illustrate the efficiency and accuracy of the proposed technique and also the results are compared with the different methods.

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A new numerical method for a class of Volterra and Fredholm integral equations

Cited by 9 publications

References 14 publications

A New Numerical Technique for Solving Volterra Integral Equations Using Chebyshev Spectral Method

A New Numerical Technique for Solving Volterra Integral Equations Using Chebyshev Spectral Method

A novel super-convergent numerical method for solving nonlinear Volterra integral equations based on B-splines

A numerical solution of Volterra integral-algebraic equations using Bernstein polynomials

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