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Further results on Ulam stability for a system of first-order nonsingular delay differential equations

Zada Akbar, Pervaiz Bakhtawar, Alzabut Jehad, Shah Syed Omar

Demonstratio Mathematica

2020

Vol. 53, nr 1

225--235

This paper is concerned with a system governed by nonsingular delay differential equations. We study the β-Ulam-type stability of the mentioned system. The investigations are carried out over compact and unbounded intervals. Before proceeding to the main results, we convert the system into an equivalent integral equation and then establish an existence theorem for the addressed system. To justify the application of the reported results, an example along with graphical representation is illustrated at the end of the paper.

Inversion of Square Matrices in Processors With Limited Calculation Abillities

Janiszowski K. B.

International Journal of Applied Mathematics and Computer Science

2003

Vol. 13, no 2

199-204

An iterative inversion algorithm for a class of square matrices is derived and tested. The inverted matrix can be defined over both real and complex fields. This algorithm is based only on the operations of addition and multiplication. The numerics of the algorithm can cope with a short number representation and therefore can be very useful in the case of processors with limited possibilities, like different neuro-computers and accelerator cards. The quality of inversion can be traced and tested. The algorithm can be used in the case of singular matrices, and then it automatically produces a result that contains the inverse of this part of the processed matrix which can be inverted. An example of the inversion of a six-order square matrix is presented and discussed.