Multistep Collocation Method for a Class of Nonstandard Volterra Integral Equations

This paper investigates the multistep collocation method for a class of nonstandard Volterra integral equations and analyzes the convergence order of the numerical solutions. By constructing collocation solutions in piecewise polynomial spaces and introducing a multistep scheme, it is proved that the solution is uniformly bounded under appropriate collocation parameters. Furthermore, the global and local optimal convergence orders of the collocation solution are derived. Both theoretical and numerical results demonstrate that the multistep collocation method achieves high numerical accuracy and reliability in solving nonstandard Volterra integral equations.