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Physical Sciences and Mathematics Commons

Open Access. Powered by Scholars. Published by Universities.®

Mathematics

TÜBİTAK

Journal

2018

Stability

Articles 1 - 2 of 2

Full-Text Articles in Physical Sciences and Mathematics

An Effective Application Of Differential Quadrature Method Based Onmodified Cubic B-Splines To Numerical Solutions Of The Kdv Equation, Ali̇ Başhan Jan 2018

An Effective Application Of Differential Quadrature Method Based Onmodified Cubic B-Splines To Numerical Solutions Of The Kdv Equation, Ali̇ Başhan

Turkish Journal of Mathematics

In this study, numerical solutions of the third-order nonlinear Korteweg--de Vries (KdV) equation are obtained via differential quadrature method based on modified cubic B-splines. Five different problems are solved. To show the accuracy of the proposed method, $L_{2}$ and $L_{\infty }$ error norms of the problem, which has an analytical solution, and three lowest invariants are calculated and reported. The obtained solutions are compared with some earlier works. Stability analysis of the present method is also given.


Exponential Stability Of Periodic Solutions Of Recurrent Neural Networks With Functional Dependence On Piecewise Constant Argument, Marat Akhmet, Duygu Aruğaslan Çi̇nçi̇n, Nur Cengi̇z Jan 2018

Exponential Stability Of Periodic Solutions Of Recurrent Neural Networks With Functional Dependence On Piecewise Constant Argument, Marat Akhmet, Duygu Aruğaslan Çi̇nçi̇n, Nur Cengi̇z

Turkish Journal of Mathematics

In this study, we develop a model of recurrent neural networks with functional dependence on piecewise constant argument of generalized type. Using the theoretical results obtained for functional differential equations with piecewise constant argument, we investigate conditions for existence and uniqueness of solutions, bounded solutions, and exponential stability of periodic solutions. We provide conditions based on the parameters of the model.