Dynamic Iterations for Nonlinear Systems Applied in Population Dynamics

We investigate the application of dynamic iterations to nonlinear systems of differential equations. Such an application allows to use implicit time integration methods without solving nonlinear algebraic equations at each time step. Another advantage of the application of dynamic iterations is that the resulting numerical schemes can be solved in parallel computing environments. We conclude that the sequence of how the dynamic iterations are applied is significant and influences their rate of convergence to the solution of the given system of nonlinear differential equations. This conclusion is illustrated by numerical experiments involving Volterra equations for predator-prey interactions. We also conclude that the proposed numerical scheme is faster than the variable order method.