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Computational Methods in Applied Mathematics

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Legendre Collocation Method for Volterra Integro-Differential Algebraic Equation

Yunxia Wei / Yanping Chen
  • Corresponding author
  • School of Mathematical Sciences, South China Normal University, Guangzhou 510631, P. R. China
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/ Yunqing Huang
  • Hunan Key Laboratory for Computation and Simulation in Science and Engineering, School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, P. R. China
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Published Online: 2018-06-21 | DOI: https://doi.org/10.1515/cmam-2018-0016

Abstract

In this work we study the numerical solution to the Volterra integro-differential algebraic equation. Two numerical examples based on the Legendre collocation scheme are designed. It follows from the convergence proof and numerical experiments that the errors of the approximate solution and the errors of the approximate derivative of the solution decay exponentially.

Keywords: Volterra Integro-Differential Algebraic Equation; Legendre Collocation Discretization; Numerical Experiments; Exponential Decay

MSC 2010: 65R20; 45J05

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About the article

Received: 2017-10-01

Revised: 2018-06-01

Accepted: 2018-06-05

Published Online: 2018-06-21


Funding Source: National Natural Science Foundation of China

Award identifier / Grant number: 11671157

Award identifier / Grant number: 91430213

Funding Source: Shandong Province

Award identifier / Grant number: ZR2017MA005

This work is supported by National Natural Science Foundation of China (11671157, 91430213) and Shandong Province Natural Science Foundation of China (ZR2017MA005).


Citation Information: Computational Methods in Applied Mathematics, ISSN (Online) 1609-9389, ISSN (Print) 1609-4840, DOI: https://doi.org/10.1515/cmam-2018-0016.

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