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A semi-discrete scheme for solving fourth-order partial integro-differential equation with a weakly singular kernel using Legendre wavelets method

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Abstract

In this paper, a semi-discrete scheme is presented for solving fourth-order partial integro-differential equations with a weakly singular kernel. The second-order backward difference formula is used to discretize the temporal derivatives. After discretizing the temporal derivatives, the considered problems are converted into a set of ordinary differential equations which are solved by using Legendre wavelets collocation method. The stability and convergence properties related to the time discretization are discussed and theoretically proven. Several numerical examples are included to demonstrate the accuracy and efficiency of the proposed method.

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Authors and Affiliations

  1. College of Mathematics and Computer Science, Hunan Normal University, Changsha, 410081, People’s Republic of China

    Xiaoyong Xu & Da Xu

  2. School of Science, East China University of Technology, Nanchang, 330013, People’s Republic of China

    Xiaoyong Xu

Authors
  1. Xiaoyong Xu
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  2. Da Xu
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Correspondence to Xiaoyong Xu.

Additional information

Communicated by Antonio José Silva Neto.

Supported by the National Natural Science Foundation of China (Grant numbers: 11601076, 11671131) and the Construct Program of the Key Discipline in Hunan Province.

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Xu, X., Xu, D. A semi-discrete scheme for solving fourth-order partial integro-differential equation with a weakly singular kernel using Legendre wavelets method. Comp. Appl. Math. 37, 4145–4168 (2018). https://doi.org/10.1007/s40314-017-0566-2

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  • DOI: https://doi.org/10.1007/s40314-017-0566-2

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