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An h-p version of the continuous Petrov-Galerkin method for Volterra delay-integro-differential equations

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Abstract

We consider an h-p version of the continuous Petrov-Galerkin time stepping method for Volterra integro-differential equations with proportional delays. We derive a priori error bounds in the L 2-, H 1- and L ∞-norm that are explicit in the local time steps, the local approximation orders, and the local regularity of the exact solution. Numerical experiments are presented to illustrate the theoretical results.

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Acknowledgment

The authors would like to thank the two anonymous reviewers for many constructive and valuable suggestions, which considerably improved the presentation of the paper.

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Authors and Affiliations

  1. Department of Mathematics, Shanghai Normal University, Shanghai, 200234, China

    Lina Wang & Lijun Yi

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  1. Lina Wang
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  2. Lijun Yi
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Correspondence to Lijun Yi.

Additional information

Communicated by: Paul Houston

The work of Lijun Yi is supported in part by the National Natural Science Foundation of China (Nos. 11301343 and 11571238), the Natural Science Foundation of Shanghai Normal University (No. DYL201703), and the Natural Science Foundation of Shanghai (No. 15ZR1430900)

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Wang, L., Yi, L. An h-p version of the continuous Petrov-Galerkin method for Volterra delay-integro-differential equations. Adv Comput Math 43, 1437–1467 (2017). https://doi.org/10.1007/s10444-017-9531-2

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  • DOI: https://doi.org/10.1007/s10444-017-9531-2

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