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Numerical asymptotic stability for the integro-differential equations with the multi-term kernels

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  • Xu, Da

Abstract

We prove that a second order backward difference semi-discretization approximation for the integro-differential equations with the multi-term kernels preserves the weighted asymptotic integrabilities of continuous solutions. The method of proof extend and simulate numerically those introduced by Hannsgen and Wheeler, relying on deep frequency domain techniques.

Suggested Citation

  • Xu, Da, 2017. "Numerical asymptotic stability for the integro-differential equations with the multi-term kernels," Applied Mathematics and Computation, Elsevier, vol. 309(C), pages 107-132.
    • Handle: RePEc:eee:apmaco:v:309:y:2017:i:c:p:107-132
    DOI: 10.1016/j.amc.2017.03.046
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    Cited by:

    1. Qiao, Leijie & Xu, Da & Wang, Zhibo, 2019. "An ADI difference scheme based on fractional trapezoidal rule for fractional integro-differential equation with a weakly singular kernel," Applied Mathematics and Computation, Elsevier, vol. 354(C), pages 103-114.
    2. Fang, Xing & Qiao, Leijie & Zhang, Fengyang & Sun, Fuming, 2023. "Explore deep network for a class of fractional partial differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    3. Qiu, Wenlin & Xu, Da & Guo, Jing, 2021. "Numerical solution of the fourth-order partial integro-differential equation with multi-term kernels by the Sinc-collocation method based on the double exponential transformation," Applied Mathematics and Computation, Elsevier, vol. 392(C).

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