Abstract Efficient numerical methods using Sinc quadrature formula are proposed and analyzed for second kind Fredholm integral equations over infinite intervals. These methods are obtained by combining the infinite trapezoidal rule with two concrete families of single and double exponential transformations. In such a way, the integral equation is reduced to a set of linear algebraic equations. Furthermore, optimal error estimates of both schemes are thoroughly provided and shown to have an exponential order of convergence. Several numerical experiments are given for illustration and a comparison with well-known methods is carried out to show the outperformance of our approach in terms of accuracy and efficiency.

中文翻译：

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无限区间上第二类 Fredholm 积分方程的 Sinc-Nyström 方法

摘要 针对无限区间上的第二类Fredholm积分方程，提出并分析了使用Sinc求积公式的有效数值方法。这些方法是通过将无限梯形规则与两个具体的单指数和双指数变换族相结合而获得的。这样，积分方程就简化为一组线性代数方程。此外，彻底提供了两种方案的最佳误差估计，并显示出具有指数级收敛。给出了几个数值实验进行说明，并与众所周知的方法进行了比较，以显示我们的方法在准确性和效率方面的优越性。