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A note on rapid convergence of approximate solutions for second order periodic boundary value problems

Rahmat A. Khan, Bashir Ahmad (2005)

Archivum Mathematicum

In this paper, we develop a generalized quasilinearization technique for a nonlinear second order periodic boundary value problem and obtain a sequence of approximate solutions converging uniformly and quadratically to a solution of the problem. Then we improve the convergence of the sequence of approximate solutions by establishing the convergence of order k ( ...

A note on some characterization of invariant zeros in singular systems and algebraic criteria of nondegeneracy

Jerzy Tokarzewski (2004)

International Journal of Applied Mathematics and Computer Science

The question how the classical definition of the Smith zeros of an LTI continuous-time singular control system can be generalized and related to state-space methods is discussed. The zeros are defined as those complex numbers for which there exists a zero direction with a nonzero state-zero direction. Such a definition allows an infinite number of zeros (then the system is called degenerate). A sufficient and necessary condition for nondegeneracy is formulated. Moreover, some characterization of...

A note on the oscillation of second order differential equations

Hishyar Kh. Abdullah (2004)

Czechoslovak Mathematical Journal

We give a sufficient condition for the oscillation of linear homogeneous second order differential equation y ' ' + p ( x ) y ' + q ( x ) y = 0 , where p ( x ) , q ( x ) C [ α , ) and α is positive real number.

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