卷积核的Volterra积分方程的快速多步配置法

摘要

The fast multistep collocation methods for Volterra integral equations of Hammerstein type are constructed. The general form of multistep collocation methods is given at first. The coefficients of the methods are expressed in terms of the values of the Laplace transform of the kernel. These methods have been suitably constructed in order to be implemented in an efficient way. The order of convergence of the constructed methods is also studied. The numerical experiments confirm the expected accuracy and computational cost.%构造Hammerstein型Volterra积分方程的快速多步配置法.首先给出多步配置法的一般形式,然后利用Laplace逆变换对方法的计算过程进行改造,以减少其运算量及对计算机的存储需求,接着给出了方法的收敛性证明.数值算例验证了该方法具有收敛性好、运算效率高的特点.