A Mechanical Quadrature Method for Solving Delay Volterra Integral Equation with Weakly Singular Kernels. (16th June 2019)

• Record Type: Journal Article
• Authors: Zhang, Li; Huang, Jin; Pan, Yubin; Wen, Xiaoxia
• Other Names: Comminiello Danilo Academic Editor.
• Is Part Of: Complexity. Volume 2019(2019)
• Publication Date: 2019-06-16
• Subjects: Chaotic behavior in systems -- Periodicals; Complexity (Philosophy) -- Periodicals; 003
• DOI: 10.1155/2019/4813802
• Languages: English
• ISSNs: 1076-2787

Abstract

Abstract : In this work, a mechanical quadrature method based on modified trapezoid formula is used for solving weakly singular Volterra integral equation with proportional delays. An improved Gronwall inequality is testified and adopted to prove the existence and uniqueness of the solution of the original equation. Then, we study the convergence and the error estimation of the mechanical quadrature method. Moreover, Richardson extrapolation based on the asymptotic expansion of error not only possesses a high accuracy but also has the posterior error estimate which can be used to design self-adaptive algorithm. Numerical experiments demonstrate the efficiency and applicability of the proposed method.