In this paper, by reproducing kernel of the space W ,the Hermitean numerical solution u 2m,2n (x,y) of the dual Fredholm integral equations of second kind is constructed.It is also proved that,as the density of the no...In this paper, by reproducing kernel of the space W ,the Hermitean numerical solution u 2m,2n (x,y) of the dual Fredholm integral equations of second kind is constructed.It is also proved that,as the density of the node system increases infinitely, u 2m,2n (x,y)、u 2m,2n x′(x,y),u 2m,2n y′(x,y) and u 2m,2n xy″(x,y) ,uniformly coverge to u(x,y),u x′(x,y),u y′(x,y), and u xy″(x,y). Furthermore,the error of the approximate solution decreases monotoically in the W space norm as the nodes increases.展开更多
函数和它的傅立叶级数之间的关系,常见的有下列四种。命题1 （狄里赫勒定理）若f（x）∈C[-π,π),或在[-π,π]上只有有限个第一类间断点,并且可以把[-π,π]分为f（x）的有限个单调区间,则有f（x）=a<sub>0</sub>/2+sum f...函数和它的傅立叶级数之间的关系,常见的有下列四种。命题1 （狄里赫勒定理）若f（x）∈C[-π,π),或在[-π,π]上只有有限个第一类间断点,并且可以把[-π,π]分为f（x）的有限个单调区间,则有f（x）=a<sub>0</sub>/2+sum from i=1 to ∞（a<sub>i</sub>cosix+b<sub>i</sub>sinix）（1）其中x∈（-π,π）为f（x）的连续点,a<sub>i</sub>,b<sub>i</sub>为f（x）的傅立叶系数（以下同）。当x∈（-π,π）为f（x）的间断点时,则（1）式友端改为[f（x—0）+f（x+0）]/2。当x=±π时,则（1）式左端改为[f（-π+0）+f（π-0）]/2。命题2 若f（x）∈L<sub>2</sub>[-π,π],则对任意确定的n,有||f（x）—a<sub>0</sub>/2—sum from i=1 to n（a<sub>1</sub>cosix+bsinix）||<sub>2</sub>展开更多
基金Supported by Institution of Higher Education Scientific Research Project in Ningxia(NGY2017011)Natural Science Foundations of Ningxia(NZ15055)+1 种基金Natural Science Foundations of China(1156105511461053)
文摘In this paper, by reproducing kernel of the space W ,the Hermitean numerical solution u 2m,2n (x,y) of the dual Fredholm integral equations of second kind is constructed.It is also proved that,as the density of the node system increases infinitely, u 2m,2n (x,y)、u 2m,2n x′(x,y),u 2m,2n y′(x,y) and u 2m,2n xy″(x,y) ,uniformly coverge to u(x,y),u x′(x,y),u y′(x,y), and u xy″(x,y). Furthermore,the error of the approximate solution decreases monotoically in the W space norm as the nodes increases.
文摘函数和它的傅立叶级数之间的关系,常见的有下列四种。命题1 （狄里赫勒定理）若f（x）∈C[-π,π),或在[-π,π]上只有有限个第一类间断点,并且可以把[-π,π]分为f（x）的有限个单调区间,则有f（x）=a<sub>0</sub>/2+sum from i=1 to ∞（a<sub>i</sub>cosix+b<sub>i</sub>sinix）（1）其中x∈（-π,π）为f（x）的连续点,a<sub>i</sub>,b<sub>i</sub>为f（x）的傅立叶系数（以下同）。当x∈（-π,π）为f（x）的间断点时,则（1）式友端改为[f（x—0）+f（x+0）]/2。当x=±π时,则（1）式左端改为[f（-π+0）+f（π-0）]/2。命题2 若f（x）∈L<sub>2</sub>[-π,π],则对任意确定的n,有||f（x）—a<sub>0</sub>/2—sum from i=1 to n（a<sub>1</sub>cosix+bsinix）||<sub>2</sub>
