New solutions of hyperbolic telegraph equation

2021-04-01
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.
JOURNAL OF DYNAMICS AND GAMES

Suggestions

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...
Shortcuts to high symmetry solutions in gravitational theories
Deser, S; Tekin, Bayram (IOP Publishing, 2003-11-21)
We apply the Weyl method, as sanctioned by Palais' symmetric criticality theorems, to obtain those-highly symmetric-geometries amenable to explicit solution, in generic gravitational models and dimension. The technique consists of judiciously violating the rules of variational principles by inserting highly symmetric, and seemingly gauge fixed, metrics into the action, then varying it directly to arrive at a small number of transparent, indexless, field equations. Illustrations include spherically and axial...
On the reduction principle for differential equations with piecewise constant argument of generalized type
Akhmet, Marat (Elsevier BV, 2007-12-01)
In this paper we introduce a new type of differential equations with piecewise constant argument (EPCAG), more general than EPCA [K.L. Cooke, J. Wiener, Retarded differential equations with piecewise constant delays, J. Math. Anal. Appl. 99 (1984) 265-297; J. Wiener, Generalized Solutions of Functional Differential Equations, World Scientific, Singapore, 1993]. The Reduction Principle [V.A. Pliss, The reduction principle in the theory of the stability of motion, Izv. Akad. Nauk SSSR Ser. Mat. 27 (1964) 1297...
An Efficient Formula Synthesis Method with Past Signal Temporal Logic
Ergurtuna, Mert; Aydın Göl, Ebru (2019-01-01)
In this work, we propose a novel method to find temporal properties that lead to the unexpected behaviors from labeled dataset. We express these properties in past time Signal Temporal Logic (ptSTL). First, we present a novel approach for finding parameters of a template ptSTL formula, which extends the results on monotonicity based parameter synthesis. The proposed method optimizes a given monotone criteria while bounding an error. Then, we employ the parameter synthesis method in an iterative unguided for...
Forward-backward domain decomposition method for finite element solution of electromagnetic boundary value problems
Ozgun, Ozlem; Kuzuoğlu, Mustafa (Wiley, 2007-10-01)
We introduce the forward-backward domain decomposition method (FB-DDM), which is basically an improved version of the classical alternating Schwarz method with overlapping subdomains,for electromagnetic, boundary value problems. The proposed method is non-iterative in some cases involving smooth geometries, or it usually converges in a few iterations in other cases involving challenging geometries, via the utilization of the locally-conformal PML method. We report some numerical results for two- dimensional...
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: https://hdl.handle.net/11511/90744.