具有Green核的Urysohn积分方程近似解收敛的加速
Acceleration of convergence in approximate solutions of Urysohn integral equations with Green's kernels
AI总结：
本文针对具有Green核的Urysohn积分方程，提出基于偶次分段多项式插值投影的逼近方法，相比经典配置法显著提高近似解精度，并通过数值实验验证了理论结果。
摘要：
考虑非线性算子方程 $x - K(x) = f$，其中 $f$ 是给定函数，$K$ 是定义在 $L^\infty [0, 1]$ 上具有Green函数型核的Urysohn积分算子。我们应用基于插值投影到逼近空间 $\mathcal{X}_n$ 的逼近方法，该空间是关于 $[0, 1]$ 的一致划分的偶次分段多项式空间。由这些方法获得的近似解与同一方程的经典配置解相比，显示出更高的精度。给出了数值例子以支持我们的理论结果。
英文摘要：
Consider a non-linear operator equation $x - K(x) = f$, where $f$ is a given function and $K$ is a Urysohn integral operator with Green's function type kernel defined on $L^\infty [0, 1]$. We apply approximation methods based on interpolatory projections onto the approximating space $\mathcal{X}_n$, which is the space of piecewise polynomials of even degree with respect to a uniform partition of $[0, 1]$. The approximate solutions obtained from these methods demonstrate enhanced accuracy compared to the classical collocation solution for the same equation. Numerical examples are given to support our theoretical results.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
