论文标题
Cayley转换方法的加权估计方法是在Banach空间中的边界价值问题
Weighted estimates of the Cayley transform method for boundary value problems in a Banach space
论文作者
论文摘要
我们考虑了Banach空间中具有强正操作员系数的线性二阶频率的边界值问题（BVP）。该解决方案以无限序列的形式通过操作员的Cayley变换，自变量的Meixner型多项式，操作员绿色函数和方程右侧的傅立叶串联表示形式。每个问题的近似解决方案是n（或通过n）汇总的部分总和。我们证明了加权误差估计值，具体取决于离散参数n，自变量与间隔边界点的距离以及输入数据的某些平滑度属性。
We consider the boundary value problems (BVPs) for linear secondorder ODEs with a strongly positive operator coefficient in a Banach space. The solutions are given in the form of the infinite series by means of the Cayley transform of the operator, the Meixner type polynomials of the independent variable, the operator Green function and the Fourier series representation for the right-hand side of the equation. The approximate solution of each problem is a partial sum of N (or expressed through N) summands. We prove the weighted error estimates depending on the discretization parameter N, the distance of the independent variable to the boundary points of the interval and some smoothness properties of the input data.
