Multistep collocation and iterated multistep collocation methods for solving two-dimensional Volterra integral equations

摘要

In this paper, the multistep collocation and iterated multistep collocation methods are investigated for solving two-dimensional Volterra integral equations. These methods, after rectangling the domain of integration, for approximating the solution in each rectangle depend on a fixed number of approximate values of solution in previous time and spatial steps, and in collocation points in the current rectangle. Convergence order and linear stability of the methods are analyzed. Also efficiency of the methods is shown by some numerical examples.