论文标题
非线性亚伯积分方程的数值解决方案：$ hp $ - version置式方法
Numerical Solution of Nonlinear Abel Integral Equations: An $ hp $-Version Collocation Approach
论文作者
论文摘要
本文涉及第一类非线性弱单数伏特拉积分方程的数值解决方案。完全研究了非线性亚伯积分方程的存在和唯一性问题。引入了$ hp $ version搭配方法与雅各比多项式一起引入，因此可以找到适当的数值解决方案。我们对其进行了正确的分析，并在$ l^2 $ -NORM中找到错误估计。该方法的效率通过一些数值实验说明。
This paper is concerned with the numerical solution for a class of nonlinear weakly singular Volterra integral equation of the first kind. The existence and uniqueness issue of the nonlinear Abel integral equations is studied completely. An $hp$-version collocation method in conjunction with Jacobi polynomials is introduced so as an appropriate numerical solution to be found. We analyze it properly and find an error estimation in $L^2$-norm. The efficiency of the method is illustrated by some numerical experiments.
