一类Fredholm型弱奇性核积分方程的数值解

Numerical method for Fredholm type weak singular kernel integral equation

在断裂力学问题中,通过确定某些物理量之间的关系,可以将其转化为积分方程.对于具有对数函数弱奇异性积分核的一类Fredholm型I类积分方程,解的性质主要取决于方程中未知函数的形式.根据积分方程的特点,给出一种数值计算方法,并给出了数值例子,最后通过数值解与精确解的比较说明了该方法的有效性.

In the problem of fracture mechanics,the determined relation of some physics factors is often transformed to the mathematics expression of integral equation.For the Type I Fredholm integral equation with logarithm function singular integral kernel the character of the solution depends on the unknown function of integral equation.According to the character of integral equation,a numerical method and examples of numerical is given.The results of the numerical computation show the validity and practicality of the method.