Projection-algebraic approximation of linear and nonlinear operator differential equations in Banach spaces

Abstract

We develop a Calogero-type projection-algebraic method of discrete approximations for linear differential equations in Banach spaces and analyze the convergence of finite-dimensional approximations based on the functional-analytic approach to discrete approximations and methods of operator theory in Banach spaces. Applications of the obtained results to the functional-interpolation scheme of the projection-algebraic method of discrete approximations are considered. Based on a generalized Leray-Schauder-type theorem, we consider the projection-algebraic scheme of discrete approximations and analyze its solvability and convergence for a special class of nonlinear operator equations.