Qualitative behaviour of numerical approximations to Volterra integro-differential equations
The authors consider the numerical solution of a nonlinear Volterra integro-differential equation with infinite delay under numerical approximation. The equation arises as a single-species growth model and the numerical method under consideration is the composite \(\theta\) rule. The aim of the paper is to check that the qualitative behaviour of the numerical scheme reflects accurately the underlying qualitative behaviour of the original equation and to give conditions, if necessary, for this to happen. The application of a numerical method leads to a Volterra difference scheme and the authors analyse the qualitative behaviour of the difference equations. They conclude that, for small enough step sizes and for small bounded initial function, the numerical scheme reflects accurately the behaviour of the exact solution. They point out that their analysis can also be applied to other classes of equations.
nonlinear Volterra integro-differential equation
scientific article; zbMATH DE number 2107319