第二类Fredholm积分方程组的分段泰勒级数展开法

A piecewise Taylor-series Expansion Method for a System of Fredholm Integral Equations of the Second Kind

积分方程出现在数学物理的各种问题中,寻求其简单而又有效的解法显得很有必要.提出一种求解第二类线性Fredholm积分方程组的新解法,利用分段泰勒级数展开,通过引入两个参数得到近似解的表达式,并对近似解的收敛性和误差进行分析.通过与已有数值方法的比较,说明此方法的可行性和有效性。

Integral equations are arising in many branches of mathematical physics and they should be solved simply and effectively. In the present paper, a piecewise Taylor-series expansion method is proposed for numerically solving a linear system of Fredholm integral equations of the second kind. By introducing two parameters, the approximate solutions are given and their convergence and error estimate are analyzed. Some numerical results are carried out to illustrate the proposed method and compare with the existing ones. The obtained results reveal that the proposed method is simple and effective.