Volume 34, Issue 1
Strong Predictor-Corrector Methods for Stochastic Pantograph Equations

J. Comp. Math., 34 (2016), pp. 1-11.

Published online: 2016-02

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• Abstract

The paper introduces a new class of numerical schemes for the approximate solutions of stochastic pantograph equations. As an effective technique to implement implicit stochastic methods, strong predictor-corrector methods (PCMs) are designed to handle scenario simulation of solutions of stochastic pantograph equations. It is proved that the PCMs are strong convergent with order $\frac{1}{2}$. Linear MS-stability of stochastic pantograph equations and the PCMs are researched in the paper. Sufficient conditions of MS-unstability of stochastic pantograph equations and MS-stability of the PCMs are obtained, respectively. Numerical experiments demonstrate these theoretical results.

• Keywords

Stochastic pantograph equation, Predictor-corrector method, MS-convergence, MS-stability.

• AMS Subject Headings

60H10, 65C20.

fyxiao@mailbox.gxnu.edu.cn (Feiyan Xiao)

pwang@jlu.edu.cn (Peng Wang)

• BibTex
• RIS
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@Article{JCM-34-1, author = {Xiao , Feiyan and Wang , Peng}, title = {Strong Predictor-Corrector Methods for Stochastic Pantograph Equations}, journal = {Journal of Computational Mathematics}, year = {2016}, volume = {34}, number = {1}, pages = {1--11}, abstract = {

The paper introduces a new class of numerical schemes for the approximate solutions of stochastic pantograph equations. As an effective technique to implement implicit stochastic methods, strong predictor-corrector methods (PCMs) are designed to handle scenario simulation of solutions of stochastic pantograph equations. It is proved that the PCMs are strong convergent with order $\frac{1}{2}$. Linear MS-stability of stochastic pantograph equations and the PCMs are researched in the paper. Sufficient conditions of MS-unstability of stochastic pantograph equations and MS-stability of the PCMs are obtained, respectively. Numerical experiments demonstrate these theoretical results.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1506-m2014-0110}, url = {http://global-sci.org/intro/article_detail/jcm/9779.html} }
TY - JOUR T1 - Strong Predictor-Corrector Methods for Stochastic Pantograph Equations AU - Xiao , Feiyan AU - Wang , Peng JO - Journal of Computational Mathematics VL - 1 SP - 1 EP - 11 PY - 2016 DA - 2016/02 SN - 34 DO - http://doi.org/10.4208/jcm.1506-m2014-0110 UR - https://global-sci.org/intro/article_detail/jcm/9779.html KW - Stochastic pantograph equation, Predictor-corrector method, MS-convergence, MS-stability. AB -

The paper introduces a new class of numerical schemes for the approximate solutions of stochastic pantograph equations. As an effective technique to implement implicit stochastic methods, strong predictor-corrector methods (PCMs) are designed to handle scenario simulation of solutions of stochastic pantograph equations. It is proved that the PCMs are strong convergent with order $\frac{1}{2}$. Linear MS-stability of stochastic pantograph equations and the PCMs are researched in the paper. Sufficient conditions of MS-unstability of stochastic pantograph equations and MS-stability of the PCMs are obtained, respectively. Numerical experiments demonstrate these theoretical results.

Feiyan Xiao & Peng Wang. (2019). Strong Predictor-Corrector Methods for Stochastic Pantograph Equations. Journal of Computational Mathematics. 34 (1). 1-11. doi:10.4208/jcm.1506-m2014-0110
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