再生核空间中非线性算子方程的精确解

Exact solution for nonlinear operator equation in reproducing kernel space

在再生核空间W12[a,b]中讨论一类非线性算子方程的求解方法,利用再生核函数的特殊性质和升元的方法,将其转化为二维再生核空间上线性算子方程的求解。在一定的条件下,给出了这类方程的精确解,并用数值算例验证了该算法的有效性。

In the reproducing kernel space W2^1 [a,b], the method for solving a kind of nonlinear operator equations is discussed, employing the special properties of the reproducing kernel function and the dimension raising method, it is changed into the linear operator equation defined in the two - dimensional reproducing kernel space to solve. Under certain condition, the exact solution is given, and the effectiveness is shown by the numerical example.