Convergence and stability of exponential integrators for semi-linear stochastic pantograph integro-differential equations with jump

Haiyan Yuan and Cheng Song

Chaos, Solitons & Fractals, 2020, vol. 140, issue C

Abstract: The present article revisits the well-known exponential integrators for semi-linear stochastic pantograph integro-differential equations with jump. It studies the stability of exact solutions of semi-linear stochastic pantograph integro differential equations with jump first, gives the conditions which guarantee the existence and uniqueness of an exact solution. Then it constructs exponential integrators for semi-linear stochastic pantograph integro-differential equations with jump and proves that the exponential Euler method is convergent with strong order p=12. It also studies the stability of the exponential integrators and proves that the exponential Euler method can reproduce the mean-square exponential stability of the analytical solution under some restrictions on the step size. In addition, it presents some numerical experiments to confirm the theoretical results.

Keywords: Semi-linear stochastic pantograph integro-differential equation with jump; Exponential integrators; Mean-square exponential stability; Trapezoidal rule (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:140:y:2020:i:c:s0960077920305683

DOI: 10.1016/j.chaos.2020.110172

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