Telegraph Equation Research Articles

General Integral Transform Performance for Space-Time Fractional Telegraph Equations

The development of technology has supported effective tools in industrial machines and set up the remarkable phase that serves well-being such as kinetic energy, kinetic movement, and nuclear energy. Applied mathematics has also contributed valuable procedures in various fields of these sciences, especially the creation of transformation. With practical relevance, a new general integral (NGI) transform has also shown a crucial role in the same pragmatic methods. In this paper, the NGI transform using the combination of Padé approximation including continued fraction expansions (CFE) has been used to attain approximate solutions of space-time fractional telegraph equations by directly getting the inverse transform.

Nonlinear Time-domain signal and noise analysis of an active CRLH transmission line for millimeter-wave frequencies

In this paper, time domain signal and noise behavior of an active CRLH transmission line was investigated in the nonlinear regime at millimeter wave frequencies. In this structure, the transistor is considered as three coupled transmission lines and all three drain,gate and source lines are CRLH transmission lines. The left-handed element values for the active CRLH transmission line are calculated in such a way that the phase cancellation effect and dispersion of the CRLH transmission line are reduced. In order to model this active CRLH transmission line, with the assumption of wave propagation in the form of Quasi-TEM, the distributed modeling method is used to extract stochastic telegraphic equation (STE) in the non-linear regime. To model noise sources in the non-linear regime, the Wiener process and modulation functions have been used to model white noise in the nonlinear regime and in the time domain. By applying the finite integration method to stochastic telegraphic equation, the behavior of the signal and noise of the active structure CRLH has been compared with a line of active structure RH and the obtain results of the numerical method have been verified with the results of the Agilent ADS software.

The generalized telegraph equation with moving harmonic source: Solvability using the integral decomposition technique and wave aspects

The paper is devoted to study the frequency shift in the solution of the generalized telegraph equation with a moving point-wise harmonic source. This equation contains the nonlocality in time derivatives which is expressed by the memory functions η(t) and γ(t), where η(t) smears the second time-derivative and γ(t) the first one. Moreover, in the Laplace domain we have ηˆ(s)=γˆ2(s). The generalized telegraph equation with an external source is solved by using the integral decomposition which allows us to write this solution as a product of the solution of the telegrapher equation with harmonic source and fγˆ(ξ,t) which is a function of the Laplace transform of memory function γ. Such obtained solution manifests the frequency shift which is illustrated in three examples of the memory functions γ(t): the localized case, its mixture with power-law, and the power-law case only. We show that only the first two cases have the wave front and the Doppler-like shift. The third example, despite the lack of wave fronts, also manifests the frequency shift. Thus it turns out that the frequency shift occurs regardless of the existence of a wave front, but it is more visible when such a front exists.

A least squares finite element method for time fractional telegraph equation with Vieta-Lucas basis functions

We proposed a Least Squares Finite Element Method (LSFEM) for the approximate solution of Time fractional telegraph equation (TFTE). The method implemented the Vieta-Lucas polynomials expressed in the Caputo fractional sense as basis functions. The LSFEM reduces the TFTE into algebraic system with element matrices and vectors, while the Conjugate Gradient Method (CGM) solved the system for the unknowns with the aid of MAPLE 18. The results generated implies that the proposed method converges favorably to the theoretical solution when the number of elements is large with a large space-time step used for the parameter t.

A high-order space-time spectral method for the distributed-order time-fractional telegraph equation

A high-order space-time spectral method for the distributed-order time-fractional telegraph equation

Anomalous heat transport and universality in macroscopic diffusion models

Anomalous diffusion is ubiquitous in nature and relevant for a wide range of applications, including energy transport, especially in bio- and nano-technologies. Numerous approaches have been developed to describe it from a microscopic point of view, and recently, it has been framed within universality classes, characterized by the behaviour of the moments and auto-correlation functions of the transported quantities. It is important to investigate whether such universality applies to macroscopic models. Here, the spectrum of the moments of the solutions of the transport equations is investigated for three continuous PDE models featuring anomalous diffusion. In particular, we consider the transport described by: (i) a generalized diffusion equation with time-dependent diffusion coefficient; (ii) the Porous Medium Equation and (iii) the Telegrapher Equation. For each model, the key features of the source-type solution as well as the analytical results for the moment analysis are revisited and extended via both analytical and numerical approaches. Equivalence of the asymptotic behaviour of the corresponding heat transport is confirmed within the realm of weak anomalous diffusion.

A Study for Solving Pseudo-Parabolic Viscous Diffusion, Telegraph, Poisson and Helmholtz PDE using Legendre-Collocation Method

Legendre collocation approach is implemented employing the operative-differential array escorted by the shifted Legendre polynomials. The significance of the proposed approach is reducing the intended partial differential equation problem into an algebraic system of equations by the aid of Legendre polynomials as orthogonal basis. Using mesh collocation points, the domain of the resulting algebraic system solution domain is discretized, and it is then solved to obtain an approximation solution. To demonstrate the accuracy of the procedure, the maximum absolute error and the estimate error are calculated. Also, Illustrative numerical examples are demonstrated to display the veracity of the potential approach in particular pseudo-parabolic viscous diffusion, telegraph, Poisson and Helmholtz partial differential equations. The generated results are contrasted with the exact solutions/other methods to highlight the efficiency of the proposed approach.

Series Solution to Fractional Telegraph Equations Using an Iterative Scheme Based on Yang Transform

Series Solution to Fractional Telegraph Equations Using an Iterative Scheme Based on Yang Transform

A new method of failure analysis

The present paper develops a new failure analysis method under plane strain conditions considering a generalized linear yield criterion. The yield criterion and the stress equilibrium equations constitute a hyperbolic system of equations. It is shown that two auxiliary variables satisfy the equation of telegraphy. Simple analytical relationships connect these variables and the radii of curvature of the characteristic curves. The calculated radii of curvature allow for the corresponding characteristic net to be constructed. Then, the stress field is determined using another set of analytical relationships. Thus, a numerical procedure is only necessary for solving the equation of telegraphy. This equation can be integrated by the method of Riemann. In particular, Green’s function is the Bessel function of zero order. A simple example illustrates the general method.

Intermittent Kac's flights and the generalized telegrapher's equation.

A generalized one-dimensional telegrapher equationassociated with an intermittent change of sign in the velocity of a Kac's flight has been proposed. To solve this random differential equation, we used the enlarged master equationapproach to obtain the exact differential equationfor the evolution of a normalized positive distribution. This distribution is associated with a generalized finite-velocity diffusionlike process. We studied the robustness of the ballistic regime, the cutoff of its domain, and the time-dependent Gaussian convergence. The second moment for the evolution of the profile has been studied as a function of non-Poisson statistics (possibly intermittent) for the time intervals Δ_{ij} in the Kac's flight. Numerical results for the evolution of sharp and wide initial profiles have also been presented. In addition, for comparison with a non-Gaussian process at all times, we have revisited the non-Markov Poisson's flight with exponential pulses. A theory for generalized random flights with intermittent stochastic velocity and in the presence of a force is also presented, and the stationary distribution for two classes of potential has been obtained.

A High Order Numerical Scheme for Time-Fractional Telegraph Equation Via Cubic Spline in Tension

A High Order Numerical Scheme for Time-Fractional Telegraph Equation Via Cubic Spline in Tension

A new method of solving plane-strain boundary value problems for the double slip and rotation model

Abstract A method of solving plane-strain boundary value problems for a reduced version of the double slip and rotation model is developed. It is assumed that the intrinsic spin vanishes. Elastic strains are neglected. The Mohr–Coulomb yield criterion is adopted. An analogy between the solutions for this model and classical rigid plastic solutions of pressure-independent plasticity is revealed. The method is based on introducing auxiliary variables that satisfy the equation of telegraphy in regions where both families of characteristics are curved. Therefore, Riemann's method can conveniently be applied to solving boundary value problems. The method is employed for analyzing the processes of plane-strain drawing and extrusion through a wedge-shaped die. Friction is neglected. The solution is given in terms of ordinary integrals. The effect of the angle of internal friction on processes’ parameters is revealed. The solution reduces to available solutions of pressure-independent plasticity if the angle of internal friction vanishes.

Extension of Haar wavelet technique for numerical solution of three-dimensional linear and nonlinear telegraph equations

In this manuscript, a hybrid numerical technique is presented for solving three-dimensional hyperbolic telegraph equations. The proposed technique is based on the Haar wavelet collocation method and the finite difference method. In this technique, the space derivatives are estimated by truncated Haar wavelet series, while the time derivatives are approximated using finite difference method. The method is applied to some linear and non-linear three-dimensional hyperbolic telegraph equations. In the linear case, the resulting algebraic system is solved by the Gauss elimination technique. Whereas in the nonlinear case, the quasi-Newton linearization technique is utilized to remove the nonlinearity of the problem. The maximum absolute errors, root mean square errors and computational rate of convergence are calculated for a different number of collocation points at different time steps of the final time t=1. The stability analysis for the proposed method is also discussed. Overall, the recently devised numerical method boasts straightforward implementation, rapid convergence, and enhanced accuracy in addressing both linear and nonlinear problems.

Observer Design for Collocated-Boundary Measurements of Transmission Line Governed by Telegraph Equations with Application to Fault Detection

This paper addresses the problem of estimating the distributed state (i.e., current and voltage) along lossy transmission line (TL). The TL is represented by the hyperbolic-type partial differential equation (PDE), also known as Telegraph equations. To this end, we develop an observer that provides online estimates of the variables of interest, based only on collocated measurements at the ingoing boundary. The observer design relies on backstepping method involving input error injections entering the domain and boundary equations. The resulting collocated observer have explicit spatially varying gains. The distributed observer features exponential convergence and, in addition, proves to be useful for fault detection of the most frequent practical scenario, i.e., the single-phase to ground short-circuit. The observer performances are also highlighted by simulation results that illustrate the observer ability to detect and localize the fault precisely.

LOCAL FRACTIONAL SUMUDU DECOMPOSITION METHOD TO SOLVE FRACTAL PDEs ARISING IN MATHEMATICAL PHYSICS

In this paper, we investigate solutions of telegraph, Laplace and wave equations within the local fractional derivative operator by using local fractional Sumudu decomposition method. This method is coupled by the Sumudu transform and decomposition method. The method in general is easy to implement and yields good results. Illustrative examples are included to demonstrate the validity and applicability of the presented method.

The Coercive Property and a Priori Error Estimation of the Finite Element Method for Linearly Distributed Time Order Fractional Telegraph Equation with Restricted Initial Conditions

The Coercive Property and a Priori Error Estimation of the Finite Element Method for Linearly Distributed Time Order Fractional Telegraph Equation with Restricted Initial Conditions

LOCAL TIME FRACTIONAL REDUCED DIFFERENTIAL TRANSFORM METHOD FOR SOLVING LOCAL TIME FRACTIONAL TELEGRAPH EQUATIONS

In this paper, we seek to find solutions of the local time fractional Telegraph equation (LTFTE) by employing the local time fractional reduced differential transform method (LTFRDTM). This method produces a numerical approximate solution having the form of an infinite series that converges to a closed form solution in many cases. We apply LTFRDTM on four different LTFTEs to examine the efficiency of the proposed method. The yielded results established the effectiveness of LTFRDTM as a reliable and solid approach for obtaining solutions of LTFTEs. The solutions coincided with the exact solution in the ordinary case when [Formula: see text]. It also required minimal amount of computational work and saved a lot of time.

On Developing He Method with Mohand Transform to Find Numerical and Exact Solutions of Some Neutrosophic Partial Differential Equations

In this paper, we propose a novel combination of the (He) method with (Mohand transform), and this combination is summarized by representing the nonlinear part (or the residue of the operator) with (He) polynomials after applying the Mohand transform. To prove the accuracy of the proposed method, we applied it to several neutrosophic partial differential equations such as neutrosophic version of Helmholtz equation, neutrosophic version of non-linear oscillator, neutrosophic version of Burger's equation, and the neutrosophic version of telegraph equation. The accuracy and effectiveness of the application of the proposed method was verified by comparing the results obtained with other methods using the Maple software package.

Analytical solutions via coupled Elzaki adomian decomposition method for some applications

An efficient combination of Adomian Decomposition iterative technique coupled Elzaki transformation (ETADM) for solving Telegraph equation and Riccati non-linear differential equation (RNDE) is introduced in a novel way to get an accurate analytical solution. An elegant combination of the Elzaki transform, the series expansion method, and the Adomian polynomial. The suggested method will convert differential equations into iterative algebraic equations, thus reducing processing and analytical work. The technique solves the problem of calculating the Adomian polynomials. The method’s efficiency was investigated using some numerical instances, and the findings demonstrate that it is easier to use than many other numerical procedures. It has also been established that (ETADM) is a trustworthy technique for solving differential equations. Using the Mathematica 13.3 programme, the graphs of the approximate solutions are presented.

Schumann resonance anomalies associated with two (M~7) Tohoku offshore earthquakes in the spring of 2021

ABSTRACT. We describe the Schumann resonance (SR) anomalies associated with two earthquakes (EQs) observed in Japan in the spring of 2021. SR is the global electromagnetic phenomenon observed in the ELF (extremely low frequency) band, and its resonance peaks are observed in the power spectra on natural radio noise at frequencies of 8, 14, 20, Hz, etc. The natural source of ELF radiation is the global lightning activity occurring in the Earth-ionosphere cavity. The anomalies were observed for the first time in Japan for the EQs in Taiwan when the distance between the observatory and the EQ epicenter was a few Mm (1 Mm = 1000 km). Recently, a new SR anomaly was addressed, related to nearby (a few hundred km) EQs (Hayakawa et al., 2019, 2020a,b). This paper presents the SR anomalies observed in the vicinity of Nagoya-city for two relatively close (~500 km) successive EQs with magnitude around 7 that occurred offshore the Tohoku area in Japan. The anomaly is characterized by the noticeable simultaneous increase or decrease in the amplitudes of three SR modes. This SR unusual behavior was observed prior to and after each of the two EQs that occurred in February and March, 2021. Observational data were interpreted in the model of seismogenic perturbations of the lower ionospheric conductivity profile. Model computations imply the full-wave solution of the ELF electromagnetic problem in the form of the Riccati equation and the 2D (two dimensional) telegraph equations. We show that observed disturbances in the SR power spectra might be attributed to two types of seismogenic modifications in the lower ionospheric profile: the compression or the expansion of the vertical profiles of mesospheric conductivity over the EQ epicenter.