第二类非线性Fredholm型积分方程数值解

Numerical Solutions of Nonlinear Fredholm Integral Equations of the Second Kind

配置法研究了地球物理中常见的第二类非线性Fredholm型积分方程的数值解法,将第二类非线性Fredholm型积分方程转化为非线性代数方程组进行求解,采用高斯数值积分公式,给出了数值计算的具体实例。利用Matlab软件的符号运算功能编程计算,克服了非线性方程难于变成求解的困难,数值例子表明该方法编程简便有效。对非线性积分方程和非线性代数方程组的求解都有重要价值。

The collocation method is used to solve nonlinear Fredholm integral equations of the Second kind in geophysical problems. We transform nonlinear Fredholm Integral Equations into the nonlinear algebraic equations, then solve the algebraic equaitons. Numerical experiments are given with Gauss numerical integral formulas. Programming is based on the symbol function of Matlab software. This paper solves the problem of hard-programming of the nonlinear equations. Numerical experiments show the efficiency of the method. The article is valuable for solving nonlinear integral equationsand nonlinear algebraic equations.