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

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  • Yuan, Haiyan
  • Song, Cheng

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.

Suggested Citation

  • Yuan, Haiyan & Song, Cheng, 2020. "Convergence and stability of exponential integrators for semi-linear stochastic pantograph integro-differential equations with jump," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    • Handle: RePEc:eee:chsofr:v:140:y:2020:i:c:s0960077920305683
    DOI: 10.1016/j.chaos.2020.110172
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