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Linear barycentric rational collocation method for solving second-order Volterra integro-differential equation

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Abstract

Second-order Volterra integro-differential equation is solved by the linear barycentric rational collocation method. Following the barycentric interpolation method of Lagrange polynomial and Chebyshev polynomial, the matrix form of the collocation method is obtained from the discrete Volterra integro-differential equation. With the help of the convergence rate of the linear barycentric rational interpolation, the convergence rate of linear barycentric rational collocation method for solving Volterra integro-differential equation is proved. At last, several numerical examples are provided to validate the theoretical analysis.

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Acknowledgements

The work of Jin Li was supported by Natural Science Foundation of Shandong Province (Grant No. ZR2016JL006) Natural Science Foundation of Hebei Province (Grant No. A2019209533), National Natural Science Foundation of China (Grant Nos. 11471195, 11771398) and China Postdoctoral Science Foundation (Grant No. 2015T80703).

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Correspondence to Jin Li.

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Communicated by Hui Liang.

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Li, J., Cheng, Y. Linear barycentric rational collocation method for solving second-order Volterra integro-differential equation. Comp. Appl. Math. 39, 92 (2020). https://doi.org/10.1007/s40314-020-1114-z

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  • DOI: https://doi.org/10.1007/s40314-020-1114-z

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