求解广义Burgers方程的一种迭代方法

摘要

在再生核空间W(2,3)中给出了求解广义Burgers方程的一种迭代方法.证明了近似解un(t,x)收敛到精确解u(t,x).该方法是大范围收敛,即对任意的初始函数u1(t,x),un(t,x)都收敛到精确解u(t,x).并且这种迭代方法也可以用来解其它非线性算子方程.%An iterative method for solving the generalized Burgers equation is obtained in reproducing kernel space W(2,3).It is proved that the approximation solution un(t,x)converges to the exact solution u(t,x).Moreover the method is large-range convergent,namely,un(t,x)converges to the exact solution u(t,x)for any u1(t,x).It is worthy to note that the method can be generalized to solve other nonlinear operator equations.