In this work we study the appearance of spurious solutions when first-order differential equations with unimodal righthand sides are discretized using Runge-Kutta schemes. These spurious solutions are explained in terms of the iteration functions. Schemes that produce good approximating solutions for much longer times are given. © 1998 Elsevier Science B.V. All rights reserved.
Chen, B., & Solis, F. (1998). Discretizations of nonlinear differential equations using explicit finite order methods. Journal of Computational and Applied Mathematics, 90(2), 171–183. https://doi.org/10.1016/S0377-0427(98)00017-X