Numerical approximation for nonlinear stochastic pantograph equations with Markovian switching

Shaobo Zhou and Yangzi Hu

Applied Mathematics and Computation, 2016, vol. 286, issue C, 126-138

Abstract: The main aim of the paper is to prove that the implicit numerical approximation can converge to the true solution to highly nonlinear hybrid stochastic pantograph differential equation. After providing the boundedness of the exact solution, the paper proves that the backward Euler–Maruyama numerical method can preserve boundedness of moments, and the numerical approximation converges strongly to the true solution. Finally, the exponential stability criterion on the backward Euler–Maruyama scheme is given, and a high order example is provided to illustrate the main result.

Keywords: Strong convergence; Polynomial growth conditions; Moment boundedness; Backward Euler–Maruyama method; Markovian switching; Exponential stability (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:286:y:2016:i:c:p:126-138

DOI: 10.1016/j.amc.2016.03.040

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