Abstract
In this paper, by using the method of quasilinearization to discuss the periodic boundary value problem for a nonlinear singular differential system with ‘maxima’, we obtain monotone iterative sequences of approximate solutions which converge uniformly and quadratically to the solution of the nonlinear singular differential system with ‘maxima’.
Highlights
Convergence has an important role to play in the development of qualitative theory of various nonlinear system
The method of quasilinearization is a powerful technique for obtaining approximate solutions of nonlinear problems
A systematic development of the method to ordinary differential equations was provided by Bellman and Kalaba [ ], Lakshmikantham and Vatsala [ ]
Summary
Convergence has an important role to play in the development of qualitative theory of various nonlinear system. Singular differential systems introduced by Rosenbrock [ ], are studied because they have many applications in practical fields, such as non-Newtonian fluid mechanics, optimal control problems, and electrical circuits and some population growth models. By using the method of quasilinearization, in [ ], the authors investigated the uniform and quadratic convergence of the initial value problem for singular differential systems. We apply the method to the study of the convergence of periodic boundary value problem (PBVP) of singular differential systems with ‘maxima’. In Section , under suitable conditions, we prove quadratic convergence of monotone sequences to the solution of singular differential systems with ‘maxima’.
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