The Puiseux Expansion and Numerical Integration to Nonlinear Weakly Singular Volterra Integral Equations of the Second Kind

Wang, Tongke; Qin, Meng; Zhang, Zhiyue

doi:10.1007/s10915-020-01167-3

Cited by 7 publications

(1 citation statement)

References 52 publications

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“…From numerical point of view, Assari et al (2013) used a non-rectangular domain to find the numerical solution of a two-dimensional linear Fredholm integral equation of second kind. Wang et al (2020) developed an efficient numerical algorithm to solve a nonlinear VIE of second kind with weakly singular convolution kernel. The VIE was deduced from a nonlinear fractional differential equation in Assari and Dehghan (2019), where the authors used a meshless local Galerkin method to solve the model numerically.…”

Section: Introductionmentioning

confidence: 99%

Numerical Analysis of Volterra Integro-differential Equations with Caputo Fractional Derivative

Santra

Mohapatra

2021

Iran J Sci Technol Trans Sci

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This article deals with a fully discretized numerical scheme for solving fractional order Volterra integro-differential equations involving Caputo fractional derivative. Such problem exhibits a mild singularity at the initial time t ¼ 0. To approximate the solution, the classical L1 scheme is introduced on a uniform mesh. For the integral part, the composite trapezoidal approximation is used. It is shown that the approximate solution converges to the exact solution. The error analysis is carried out. Due to presence of weak singularity at the initial time, we obtain the rate of convergence is of order OðsÞ on any subdomain away from the origin whereas it is of order Oðs a Þ over the entire domain. Finally, we present a couple of examples to show the efficiency and the accuracy of the numerical scheme.

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Section: Introductionmentioning

confidence: 99%