New solutions of hyperbolic telegraph equation

İnç, Mustafa
Partohaghighi, Mohammad
Akınlar, Mehmet Ali
Weber, Gerhard-Wilhelm
We present a new method based on unification of fictitious time integration (FTI) and group preserving (GP) methods. The GP method is applied in numerically discretized ordinary differential equations obtained from application of FTI method to a given partial differential equation (PDE). The algorithm is applied to hyperbolic telegraph equation and utilizes the Cayley transformation and the Pade approximations in the Minkowski space. It avoids unauthentic solutions and ghost fixed points which is one of the advantages of the present method over other related numerical methods in the literature. The technique is tested on three specific examples for various parameter values appearing in the telegraph equation and discretization steps. Such solutions of the telegraph equation are obtained first time in this paper. Illustrative figures are provided. Efficiency of the method is determined by an error analysis which is achieved by comparing numerical solutions with exact solutions.


New Formulation and Implementation of Vibrational Self-Consistent Field Theory
Hansen, Mikkel B.; Sparta, Manuel; Seidler, Peter; Toffolı, Danıele; Christiansen, Ove (2010-01-01)
A new implementation of the vibrational self-consistent field (VSCF) method is presented on the basis of a second quantization formulation. A so-called active terms algorithm is shown to be a significant improvement over a standard implementation reducing the computational effort by one order in the number of degrees of freedom. Various types of screening provide even further reductions in computational scaling and absolute CPU time. VSCF calculations on large polyaromatic hydrocarbon model systems are pres...
Method of Lyapunov functions for differential equations with piecewise constant delay
Akhmet, Marat; ARUĞASLAN ÇİNÇİN, Duygu; Yılmaz, Elanur (2011-06-15)
We address differential equations with piecewise constant argument of generalized type [5-8] and investigate their stability with the second Lyapunov method. Despite the fact that these equations include delay, stability conditions are merely given in terms of Lyapunov functions; that is, no functionals are used. Several examples, one of which considers the logistic equation, are discussed to illustrate the development of the theory. Some of the results were announced at the 14th International Congress on C...
Improving the Accuracy of MFIE and CFIE by Using Numerically Designed Testing Functions
Karaosmanoglu, Bariscan; Ergül, Özgür Salih (2016-07-01)
We present a novel approach for improving the accuracy of the magnetic-field integral equation (MFIE) and the combined-field integral equation (CFIE) by using numerically designed testing functions. The compatibility of the MFIE and CFIE systems with the corresponding one derived from the electric-field integral equation (EFIE) is used to determine testing weights in given templates of testing directions. The designed testing functions lead to more accurate solutions in comparison to the standard discretiza...
Impulsive Hopfield-type neural network system with piecewise constant argument
Akhmet, Marat; Yılmaz, Elanur (2010-08-01)
In this paper we introduce an impulsive Hopfield-type neural network system with piecewise constant argument of generalized type. Sufficient conditions for the existence of the unique equilibrium are obtained. Existence and uniqueness of solutions of such systems are established. Stability criterion based on linear approximation is proposed. Some sufficient conditions for the existence and stability of periodic solutions are derived. An example with numerical simulations is given to illustrate our results.
Almost periodic solutions of second order neutral differential equations with functional response on piecewise constant argument
Akhmet, Marat (2013-01-01)
© 2013 L & H Scientific Publishing, LLC.We consider second order functional differential equations with generalized piecewise constant argument. Conditions for existence, uniqueness and stability of Bohr almost periodic solutions are defined. Appropriate examples which illustrate the results are provided.
Citation Formats
M. İnç, M. Partohaghighi, M. A. Akınlar, and G.-W. Weber, “New solutions of hyperbolic telegraph equation,” JOURNAL OF DYNAMICS AND GAMES, pp. 129–138, 2021, Accessed: 00, 2021. [Online]. Available: