Abstract

Some algorithm is presented for solving the convolution type Volterra integral equation of the first kind by the quadrature-sum method. We assume that the integral equation of the first kind cannot be reduced to an integral equation of the second kind but we do not assume that either the kernel or some of its derivatives at zero are unequal to zero. For the relations we propose there is given an estimate of the error of the calculated solution. Some examples of numerical experiments are presented to demonstrate the efficiency of the algorithm.

中文翻译：

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求和法求解第一类卷积型Volterra型积分方程

摘要

提出了一种用求和法求解第一类卷积型Volterra积分方程的算法。我们假定第一类积分方程不能简化为第二类积分方程，但我们不假定核或其零阶导数不等于零。对于我们建议的关系，给出了所计算解的误差的估计。给出了一些数值实验的例子，以证明该算法的有效性。