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Multi-step Chebyshev spectral collocation method for Volterra integro-differential equations

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We investigate multi-step Chebyshev spectral collocation method for Volterra integro-differential equations. We obtain numerical solution Y(t) and \(Y'(t)\) to approximate unknown function y(t) and its derivative \(y'(t)\) while Y(t) and \(Y'(t)\) keep the relation that \(Y'(t)\) is the derivative of Y(t). We discuss existence and uniqueness of the solution to corresponding discrete system. We provide convergence analysis for proposed method. Numerical experiments are carried out to confirm theoretical results.

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Authors and Affiliations

  1. Department of Applied Mathematics, Guangdong University of Finance, Guangzhou, 510521, China

    Zhendong Gu

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  1. Zhendong Gu
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Correspondence to Zhendong Gu.

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This work is supported by the Foundation for Distinguished Young Teachers in Higher Education of Guangdong Province (YQ201403), and the Provincial Foundation of Guangdong University of Finance for Maths Models Teaching Team (0000-E205010014157).

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Gu, Z. Multi-step Chebyshev spectral collocation method for Volterra integro-differential equations. Calcolo 53, 559–583 (2016). https://doi.org/10.1007/s10092-015-0162-z

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