Abstract:This paper deals with the blow-up behavior of numerical solutions to nonlinear fractional ordinary differential equations with a dissipative term. Based on the positivity preservation of the explicit L1-scheme, it is shown that for sufficiently small initial values, numerical solutions exist globally. Whereas for large initial values, numerical solutions with a suitable adaptive step strategy blow up in finite time. Finally, some numerical experiments are provided for verifying the theoretical analysis.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.