On the monotonicity and constancy of signs of some rational explicit methods for nonlinear systems of ordinary differential equations

We study one special type of explicit rational numerical methods for the solution nonlinear systems of ordinary differential equations and analyze the so-called property of constancy of signs of integration methods. This means that the inner product of approximate solutions at two adjacent points of the grid is positive for the corresponding differential equation. We establish the unconditional (i.e., for all sizes of steps) monotonicity and constancy of signs of rational methods.Published in Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 6, pp. 848–852, June, 1995.