The Stochastic Θ -Method for Nonlinear Stochastic Volterra Integro-Differential Equations
Joint Authors
Source
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-13, 13 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-10-27
Country of Publication
Egypt
No. of Pages
13
Main Subjects
Abstract EN
The stochastic Θ -method is extended to solve nonlinear stochastic Volterra integro-differential equations.
The mean-square convergence and asymptotic stability of the method are studied.
First, we prove that the stochastic Θ -method is convergent of order 1 / 2 in mean-square sense for such equations.
Then, a sufficient condition for mean-square exponential stability of the true solution is given.
Under this condition, it is shown that the stochastic Θ -method is mean-square asymptotically stable for every stepsize if 1 / 2 ≤ θ ≤ 1 and when 0 ≤ θ < 1 / 2 , the stochastic Θ -method is mean-square asymptotically stable for some small stepsizes.
Finally, we validate our conclusions by numerical experiments.
American Psychological Association (APA)
Hu, Peng& Huang, Chengming. 2014. The Stochastic Θ -Method for Nonlinear Stochastic Volterra Integro-Differential Equations. Abstract and Applied Analysis،Vol. 2014, no. 2014, pp.1-13.
https://search.emarefa.net/detail/BIM-1014266
Modern Language Association (MLA)
Hu, Peng& Huang, Chengming. The Stochastic Θ -Method for Nonlinear Stochastic Volterra Integro-Differential Equations. Abstract and Applied Analysis No. 2014 (2014), pp.1-13.
https://search.emarefa.net/detail/BIM-1014266
American Medical Association (AMA)
Hu, Peng& Huang, Chengming. The Stochastic Θ -Method for Nonlinear Stochastic Volterra Integro-Differential Equations. Abstract and Applied Analysis. 2014. Vol. 2014, no. 2014, pp.1-13.
https://search.emarefa.net/detail/BIM-1014266
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1014266