High-order convergence of multistep collocation methods for nonstandard Volterra integral equations

Abstract

Some physical and biological phenomena for the types of population growth can be modelled by nonstandard Volterra integral equations (NVIEs). In this paper, we consider multistep collocation methods to solve nonstandard Volterra integral equation and try to obtain the optimal convergence order of the numerical method. Using the fixed number of previous time steps and Lagrange basis functions, we increase the order of convergence in comparing the classical one-step collocation method. Finally, Some numerical examples are solved by multistep collocation method to illustrate the theoretical results.