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

Yongtao Zhou and Chengjian Zhang

Applied Mathematics and Computation, 2019, vol. 348, issue C, 594-608

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.

Keywords: Nonlinear stiff fractional differential equations; Caputo derivatives; Extended one-leg methods; Convergence; Stability; Numerical experiment (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:348:y:2019:i:c:p:594-608

DOI: 10.1016/j.amc.2018.12.019

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