The Numerical Method For A Class Of Fourth Order Evolutional Stochastic Differential Equations

With the progressive development of partial differential equations, it is found that realistic problem can not be solved completely by deterministic mod-els. Under this background, the theoretical analysis of stochastic equations and its numerical solutions are investigated by many mathematicians, and it has become a important topic in mathematics nowadays.In this thesis, we shell consider the numerical solution of following fourth-order linear stochastic differential equation:In the first chapter, we shell introduce the semigroup theory of stochastic partial equations. We shell present some basic theoretical results of stochastic equations in chapter two. In the third chapter, we shell give the numerical solution of finite element framework about deterministic problem, and then discuss the Argyris element. In the final chapter, we analyze the approximation problem for stochastic differential equations and carry out the numerical experiments.