Numerical Algorithm For Fractional Stochastic Integro-differential Equations

Fractional stochastic calculus equation is one of the hot topics in recent years.Due to the particularity of fractional calculus operator with non-local heritability and memory,it can be used to describe many natural phenomena in nature.Compared with the model about fractional calculus equation and the integral stochastic calculus equation model,the fractional stochastic integral and differential equation model can better reflect many natural phenomena and laws in the real world,so it is applied to random dynamic system,fluid mechanics and other fields.The first problem of this paper is studied for an effective numerical algorithm of fractional integro-differential equation that based on the shifted Legendre polynomials,the combination of the Gauss-Legendre quadrature rule and the idea of the spectral collocation method.Then,to estimate the error of the numerical algorithm,which was verified from some numerical examples.The second problem of this paper is studied for an effective numerical algorithm of the two dimensional integral equation,which is based on the idea of the first problem.Then,the error of the numerical scheme is estimated.Finally,the validity of the method is proved by some numerical examples.The third problem is studied for an effective numerical algorithm of the form of fractional stochastic integro-differential equation,which is based on the ideas of the previous two chapters.Then,the error of the numerical scheme is estimated.Finally,some numerical examples are used to verify the validity of the method.