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Implicit-explicit one-leg methods for nonlinear stiff neutral equations

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  • Tan, Zengqiang
  • Zhang, Chengjian

Abstract

In this paper, by adapting the underlying implicit-explicit (IMEX) one-leg methods (cf. [1, 2]), a class of extended IMEX one-leg (EIEOL) methods are suggested for solving nonlinear stiff neutral equations (SNEs). It is proven under some suitable conditions that EIEOL methods are D-convergent of order 2 and stable for nonlinear SNEs. Several numerical examples are given to testify the obtained theoretical results and the computational effectiveness of EIEOL methods. Moreover, a comparison with the fully implicit one-leg methods is presented, which shows that EIEOL methods have the higher computational efficiency.

Suggested Citation

  • Tan, Zengqiang & Zhang, Chengjian, 2018. "Implicit-explicit one-leg methods for nonlinear stiff neutral equations," Applied Mathematics and Computation, Elsevier, vol. 335(C), pages 196-210.
    • Handle: RePEc:eee:apmaco:v:335:y:2018:i:c:p:196-210
    DOI: 10.1016/j.amc.2018.04.046
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    References listed on IDEAS

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    1. Qin, Tingting & Zhang, Chengjian, 2015. "Stable solutions of one-leg methods for a class of nonlinear functional-integro-differential equations," Applied Mathematics and Computation, Elsevier, vol. 250(C), pages 47-57.
    2. Bellen, Alfredo & Zennaro, Marino, 2003. "Numerical Methods for Delay Differential Equations," OUP Catalogue, Oxford University Press, number 9780198506546.
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    Cited by:

    1. Tan, Zengqiang & Zhang, Chengjian, 2022. "Numerical approximation to semi-linear stiff neutral equations via implicit–explicit general linear methods," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 196(C), pages 68-87.
    2. Zhou, Yongtao & Zhang, Chengjian, 2019. "One-leg methods for nonlinear stiff fractional differential equations with Caputo derivatives," Applied Mathematics and Computation, Elsevier, vol. 348(C), pages 594-608.

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