第一类Volterra积分方程的广义多步配置法

Generalized Multistep Collocation Methods for the First-Kind Volterra Integral Equations

Volterra积分方程广泛应用在许多科学研究领域,例如热传导模型、声学散射问题、人口预测模型等。针对第一类Volterra积分方程的数值解,在经典多步配置法的基础上利用边值方法的思想,研究其广义多步配置方法。利用Lagrange插值公式,选取不同的节点作为插值节点,将原方程离散成为一个线性方程组。通过实验验证了该方法求解第一类Volterra积分方程的有效性,并且该方法可以达到较高的收敛阶。

The Volterra integral equation is widely used in many scientific research fields, such as heat transfer models, acoustic scattering problems, population prediction models and so on. Aiming at the numerical solution of the first type of Volterra integral equation, the idea of edge value method is used to study its generalized multistep collocation method based on the classical multistep collocation method. Using the Lagrange interpolation formula, different nodes are selected as interpolation nodes to discretize the original equation into a linear equation system. The effectiveness of the method in solving the first type of Volterra integral equation is verified by experiments, and the method can reach a higher convergence order.