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One-leg methods for nonlinear stiff fractional differential equations with Caputo derivatives

Author

Listed:
  • Zhou, Yongtao
  • Zhang, Chengjian

Abstract

This paper is concerned with numerical solutions for a class of nonlinear stiff fractional differential equations (SFDEs). By combining the underlying one-leg methods with piecewise linear interpolation, a type of extended one-leg methods for nonlinear SFDEs with γ-order (0 < γ < 1) Caputo derivatives are constructed. It is proved under some suitable conditions that the extended one-leg methods are stable and convergent of order min{p,2−γ}, where p is the consistency order of the underlying one-leg methods. Several numerical examples are given to illustrate the computational efficiency and accuracy of the methods.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:348:y:2019:i:c:p:594-608
    DOI: 10.1016/j.amc.2018.12.019
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    References listed on IDEAS

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    1. Wang, Wansheng, 2017. "On A-stable one-leg methods for solving nonlinear Volterra functional differential equations," Applied Mathematics and Computation, Elsevier, vol. 314(C), pages 380-390.
    2. 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.
    3. 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.
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