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THE ASYMPTOTIC THEORY OF SEMILINEAR PERTURBED telegraph equation AND ITS APPLICATION

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Applied Mathematics and Mechanics(English Edition) 1997年第7期18卷 657-662页

作者：赖绍永 Department of Mathematics Sichuan Normal University Chengdu P. R. China

This paper is devoted to studying the asymptotic theory of initial value problems for a semilinear perturbed telegraph equation. The asymptotic theory and validity of formal approximations are constructed on long timescale O(\epsilon\(-1)). As an application of the asymptotic theory, the initial value problems for a special telegraph equation are studied and two asymptotic solutions of order O(\epsilon\(-)1) are presented.

关键词： telegraph equation asymptotic theory long timescale application

Two-Dimensional Legendre Wavelets for Solving Time-Fractional telegraph equation

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Advances in Applied Mathematics and Mechanics 2014年第2期6卷 247-260页

作者： M.H.Heydari M.R.Hooshmandasl F.Mohammadi Faculty of Mathematics Yazd UniversityYazdIran Department of Mathematics Faculty of SeiencesHormozgan UniversityBandarabbasIran

In this paper,we develop an accurate and efficient Legendre wavelets method for numerical solution of the well known time-fractional telegraph *** the proposed method we have employed both of the operational matrices of fractional integration and differentiation to get numerical solution of the time-telegraph *** power of this manageable method is *** the use of Legendre wavelet is found to be accurate,simple and fast.

关键词： telegraph equation Legendre wavelets fractional calculus Caputo derivative.

Finite Element Orthogonal Collocation Approach for Time Fractional telegraph equation with Mamadu-Njoseh Polynomials

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Journal of Applied Mathematics and Physics 2023年第9期11卷 2585-2596页

作者： Ebimene James Mamadu Henrietta Ify Ojarikre Edith Omamuyovwi Maduku Department of Mathematics Delta State University Abraka Nigeria

Finite element method (FEM) is an efficient numerical tool for the solution of partial differential equations (PDEs). It is one of the most general methods when compared to other numerical techniques. PDEs posed in a variational form over a given space, say a Hilbert space, are better numerically handled with the FEM. The FEM algorithm is used in various applications which includes fluid flow, heat transfer, acoustics, structural mechanics and dynamics, electric and magnetic field, etc. Thus, in this paper, the Finite Element Orthogonal Collocation Approach (FEOCA) is established for the approximate solution of Time Fractional telegraph equation (TFTE) with Mamadu-Njoseh polynomials as grid points corresponding to new basis functions constructed in the finite element space. The FEOCA is an elegant mixture of the Finite Element Method (FEM) and the Orthogonal Collocation Method (OCM). Two numerical examples are experimented on to verify the accuracy and rate of convergence of the method as compared with the theoretical results, and other methods in literature.

关键词： Sobolev Space Finite Element Method Mamadu-Njoseh Polynomials Orthogonal Collocation Method telegraph equation

Space Discretization of Time-Fractional telegraph equation with Mamadu-Njoseh Basis Functions

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Applied Mathematics 2022年第9期13卷 760-773页

作者： Ebimene James Mamadu Ignatius Nkonyeasua Njoseh Henrietta Ify Ojarikre Department of Mathematics Delta State University Abraka Nigeria

In this paper, we examine the space discretization of time fractional telegraph equation (TFTE) with Mamadu-Njoseh orthogonal basis functions. For ease and convenience, we deal with the fractional derivative by first converting from Caputo’s type to Riemann-Liouville’s type. The proposed method was constrained to precise error analysis to establish the accuracy of the method. Numerical experimentation was implemented with the aid of MAPLE 18 to show convergence of the method as compared with the analytic solution.

关键词： Finite Difference Method Mamadu-Njoseh Polynomials telegraph equation Gaussian Elimination Method Quadrature Formula Sobolev Space

telegraph equations and Complementary Dirac equation from Brownian Movement

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Journal of Modern Physics 2012年第9期3卷 989-993页

作者： Balwant Singh Rajput Physics Department Kumaon UniversityNainitalIndia I-11 Gamma-IIGreater Noida(UP)India

telegraph equations describing the particle densities in Brownian movement on a lattice site have been derived and it has been shown that the complementary classical Dirac equation appears naturally as the consequence of correlations in particle trajectories in Brownian movement. It has also been demonstrated that Heisenberg uncertainty relation between energy and time is the necessary and sufficient condition to transform this classical equation into usual Dirac’s relativistic quantum equation.

关键词： telegraph equation Dirac equation Brownian Motion Analytic Continuation Schrodinger equation Uncertainty Relations

An Efficient Meshless Method for Hyperbolic telegraph equations in (1 + 1) Dimensions

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Computer Modeling in Engineering & Sciences 2021年第8期128卷 687-698页

作者： Fuzhang Wang Enran Hou Imtiaz Ahmad Hijaz Ahmad Yan Gu College of Mathematics and Statistics Xuzhou University of TechnologyXuzhou221018China College of Mathematics Huaibei Normal UniversityHuaibei235000China Department of Mathematics University of SwabiSwabi25000Pakistan Department of Basic Sciences University of Engineering and TechnologyPeshawar25000Pakistan College of Mathematics Qingdao UniversityQingdao266071China

Numerical solutions of the second-order one-dimensional hyperbolic telegraph equations are presented using the radial basis *** purpose of this paper is to propose a simple novel direct meshless scheme for solving hyperbolic telegraph *** is fulfilled by considering time variable as normal space *** this scheme,there is no need to remove time-dependent variable during the whole solution *** the numerical solution accuracy depends on the condition of coefficient matrix derived from the radial basis function *** propose a simple shifted domain method,which can avoid the full-coefficient interpolation matrix *** experiments performed with the proposed numerical scheme for several second-order hyperbolic telegraph equations are presented with some discussions.

关键词： Radial basis functions telegraph equation shifted domain method meshless method

SYMPLECTIC SCHEMES FOR telegraph equationS

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Journal of Computational Mathematics 2016年第3期34卷 285-299页

作者： Yi Lu Yaolin Jiang School of Mathematics and Statistics Xi'an Jiaotong University Shaanxi 710049 China

A new numerical algorithm for telegraph equations with homogeneous boundary con- ditions is proposed. Due to the damping terms in telegraph equations, there is no royal conservation law according to Noether＇s theorem. The algorithm origins from the discovery of a transform applied to a telegraph equation, which transforms the telegraph equation to a Klein-Gordon equation. The Symplectic method is then brought in this algorithm to solve the Klein-Gordon equation, which is based on the fact that the Klein-Gordon equation with the homogeneous boundary condition is a perfect Hamiltonian system and the symplectic method works very well for Hamiltonian systems. The transformation itself and the inverse transformation theoretically bring no error to the numerical computation. Therefore the error only comes from the symplectic scheme chosen. The telegraph equation is finally explicitly computed when an explicit symplectic scheme is utilized. A relatively long time result can be expected due to the application of the symplectic method. Mean- while, we present order analysis for both one-dimensional and multi-dimensional cases in the paper. The efficiency of this approach is demonstrated with numerical examples.

关键词： telegraph equation Klein-Gordon equation Symplectic method Explicitmethod.

An Exact Solution of telegraph equations for Voltage Monitoring of Electrical Transmission Line

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Energy and Power Engineering 2022年第11期14卷 669-679页

作者： Daouda Konane Wend Yam Serge Boris Ouedraogo Toussaint Tilado Guingane Abdoulaye Zongo Zacharie Koalaga François Zougmoré Laboratoire de Matériauxet Environnement (LAME) Université Joseph KI-ZERBO Ouagadougou Burkina Faso Direction de la Distribution Société Nationale de l’Electricité du Burkina (SONABEL) Ouagadougou Burkina Faso

telegraph equations are derived from the equations of transmission line theory. They describe the relationships between the currents and voltages on a portion of an electric line as a function of the linear constants of the conductor (resistance, conductance, inductance, capacitance). Their resolution makes it possible to determine the variation of the current and the voltage as a function of time at each point of the line. By adopting a general sinusoidal form, we propose a new exact solution to the telegraphers’ partial differential equations. Different simulations have been carried out considering the parameter of the 12/20 (24) kV Medium Voltage Cable NF C 33,220. The curves of the obtained solution better fit the real voltage curves observed in the electrical networks in operation.

关键词： telegraph equation Electric Network Voltage Variation Electrical Transmission Lines Analytical Solution

Numerical Solution for a Non-Fickian Diffusion in a Periodic Potential

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Communications in Computational Physics 2013年第2期13卷 502-525页

作者： Adérito Araújo Amal K.Das Cidália Neves Ercília Sousa CMUC Department of MathematicsUniversity of Coimbra3001-454 CoimbraPortugal Department of Physics DalhousieUniversityHalifaxNova Scotia B3H3J5Canada ISCAC Polytechnic Institute of Coimbra3040-316 CoimbraPortugal

Numerical solutions of a non-Fickian diffusion equation belonging to a hyperbolic type are presented in one space *** Brownian particle modelled by this diffusion equation is subjected to a symmetric periodic potential whose spatial shape can be varied by a single *** consider a numerical method which consists of applying Laplace transform in time;we then obtain an elliptic diffusion equation which is discretized using a finite difference *** analyze some aspects of the convergence of the *** results for particle density,flux and mean-square-displacement(covering both inertial and diffusive regimes)are presented.

关键词： Numerical methods Laplace transform telegraph equation periodic potential non-Fickian diffusion