In this paper, we propose an efficient B-spline finite element method for a class of fourth order nonlinear differential equations with variable coefficient. For the temporal discretization, we choose the Crank-Nicolson scheme. Boundedness and error estimates are rigorously derived for both semi-discrete and fully discrete schemes. A numerical experiment confirms our 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.