随机Kuramoto-Sivashinsky方程数值解的收敛性

Concergence of Numerical Solution for a Stochastic Kuramoto-Sivashinsky Equation

文章讨论了一类随机Kuramoto-Sivashinsky方程解数值解的收敛性.随机Kuramo-to-Sivashinsky方程一般没有解析解,所以数值近似计算成为求其解的有利方法.我们利用Ito公式,Burkholder-Davis-Gundy不等式,Gronwall引理等证明了数值解收敛到精确解.

We discuss the convergence of numerical solution for a class of stochastic Kuramoto-Sivashinsky eqution. In general, stochastic Kuramoto-Sivashinsky equation do not have explicit solut-ions,thus numerical approximation schemes are invaluable tools for exploring prop- erties. We use Ito formula,Burkholder-Davis-Gundy inequality and Gronwall lemma to prove that the numerical solution is converges to ture solution.