第二类Hammerstein积分方程的一种新解法

A New Method for Solving a Hammerstein Integral Equation of the Second Kind

摘要: 本文研究一种非线性第二类Hammerstein积分方程。在Banach空间上使用不动点原理研究其解的唯一性，基于积分中值定理和分段逼近的思想提出一种新的数值方法，构造了近似解并分析了其收敛性和误差估计。几个数值实例阐明了该方法的可行性和有效性。

Abstract: A nonlinear Hammerstein integral equation of the second kind is investigated in the present paper. The uniqueness of solution is considered by using the fixed point theorem in Banach spaces. A new numerical method is proposed by using the integral mean value theorem and the idea of piecewise approximation. An approximate solution is made and its convergence and error estimate are fur-ther analyzed. Numerical results are carried out to verify the feasibility and novelty of the proposed solution procedures.