Investigation On Conservative Numerical Methods For Stochastic Fractional Nonlinear Schr(?)dinger Equation

Stochastic differential equations(SDEs)are one of the core hot issue,which can describe the evolution of the stochastic complex system more accurately.Among the research for the SDEs,it plays the core role to construct and analyse the numerical methods for them.Besides,the fractional differential equations have got great attention,and in turn have been applied in various fields such as physics,biology and control engineering.The nonlinear Schr(?)dinger equation is not only the most classic and significant equation in quantum mechanics but also massively applied in fluid mechanics,population dynamics and so on.What's more,the stochastic fractional nonlinear Schr(?)dinger equation is an important equation for describing the open nonlocal quantum mechanics.In this article the stochastic fractional nonlinear Schr(?)dinger equation with multiplicative noise is studied:·For stochastic fractional nonlinear Schr(?)dinger equation,we prove that it admits the mass and generalized multi-symplectic coservation law.Subsequently we proposed a mass and multi-symplectic conserving method whose accuracy and conservative properties are proven by theoretical analysis and numerical experiments.·For stochastic fractional nonlinear Schr(?)dinger equation,we construct an explicit mass-conserving splitting scheme which is efficient and convenient to be adapted to high-dimensional cases.·Using invariant energy quadratization,we proposed a Mass and energy conservative high order diagonally implicit Runge-Kutta schemes for nonlinear Schr(?)dinger equation.