Abstract:The projection-algebraic approach of the Calogero type for discrete approximations of linear and nonlinear differential operator equations in Banach spaces is studied. The solution convergence and realizability properties of the related approximating schemes are analyzed. For the limiting-dense approximating scheme of linear differential operator equations a new convergence theorem is stated. In the case of nonlinear differential operator equations the effective convergence conditions for the approximated solution sets, based on a Leray-Schauder type fixed point theorem, are obtained. 1. The projection-algebraic method of discrete approximations for linear differential operator equations
MSC:
Preliminaries: a Lie-algebraic scheme of the Calogero typeA projection-algebraic approach to discrete approximations of differential operator equations has been proposed by F. Calogero in 1983 for calculating the eigenvalues of linear differential operators [5,7] in Hilbert spaces. There were *
The solution set, realizability and convergence of the projection-algebraic method of discrete approximations for linear and nonlinear differential operator equations are studied.
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.