Lagrange stability and numerical method for solving semilinear descriptor equations

Abstract

Sufficient conditions of the global solvability and the Lagrange stability of semilinear descriptor equations with regular characteristic pencil of index 1 is found. The Lagrange stability means that all solutions of an equation are bounded on the whole domain. The nonlinear right side of the equation is not required to satisfy the constraints of the global Lipschitz condition type. The numerical method for solving the descriptor equation is proposed. The mathematical model of nonlinear radio engineering filter is considered as application. The obtained numerical solutions verify the results of theoretical investigations.