In this paper,first,Bernstein multi-scaling polynomials(BMSPs)and their properties are introduced.These polynomials are obtained by compressing Bernstein polynomials(BPs)under sub-intervals.Then,by using these polynom...In this paper,first,Bernstein multi-scaling polynomials(BMSPs)and their properties are introduced.These polynomials are obtained by compressing Bernstein polynomials(BPs)under sub-intervals.Then,by using these polynomials,stochastic operational matrices of integration are generated.Moreover,by transforming the stochastic integral equation to a system of algebraic equations and solving this system using Newton’s method,the approximate solution of the stochastic Ito^(^)-Volterra integral equation is obtained.To illustrate the efficiency and accuracy of the proposed method,some examples are presented and the results are compared with other methods.展开更多
文摘In this paper,first,Bernstein multi-scaling polynomials(BMSPs)and their properties are introduced.These polynomials are obtained by compressing Bernstein polynomials(BPs)under sub-intervals.Then,by using these polynomials,stochastic operational matrices of integration are generated.Moreover,by transforming the stochastic integral equation to a system of algebraic equations and solving this system using Newton’s method,the approximate solution of the stochastic Ito^(^)-Volterra integral equation is obtained.To illustrate the efficiency and accuracy of the proposed method,some examples are presented and the results are compared with other methods.
基金Supported in part by NSF Grants(11471105)of China,NSF Grants of Hubei Province(2016CFB526)Innovation Team of the Educational Department of Hubei Province(T201412)Innovation Items of Hubei Normal University(2018032,2018105)
基金supported by the National Natural Science Foundation of P.R.China(Grant Nos.11271312,11261058)the China Postdoctoral Science Foundation(Grant Nos.20110491750)the Natural Science Foundation of Xinjiang(Grant Nos.2012211B07,2011211B08)
基金The Excellent Youth Foundation of Educational Committee of Hunan Provincial (08B005)the Hunan Postdoctoral Scientic Program(2009RS3020)+1 种基金the Scientic Research Funds of Hunan Provincial Education Department of China(09C059)the Scientic Research Funds of Hunan Provincial Science and Technology Department of China(2009FJ3103,2009ZK4021)
