scholarly journals Laplace Transform Collocation Method for Solving Hyperbolic Telegraph Equation

2017 ◽  
Vol 2017 ◽  
pp. 1-9
Author(s):  
Adebayo O. Adewumi ◽  
Saheed O. Akindeinde ◽  
Adebayo A. Aderogba ◽  
Babatunde S. Ogundare
Keyword(s):  
Laplace Transform ◽  
Collocation Method ◽  
Analytical Solutions ◽  
Trial Function ◽  
Numerical Scheme ◽  
Telegraph Equation ◽  
One Dimensional ◽  
Laplace Transform Technique ◽  
Telegraph Equations ◽  
New Form

This article presents a new numerical scheme to approximate the solution of one-dimensional telegraph equations. With the use of Laplace transform technique, a new form of trial function from the original equation is obtained. The unknown coefficients in the trial functions are determined using collocation method. The efficiency of the new scheme is demonstrated with examples and the approximations are in excellent agreement with the analytical solutions. This method produced better approximations than the ones produced with the standard weighted residual methods.

ANALYTICAL SOLUTIONS TO BRAJINSKII'S EQUATIONS FOR NUCLEAR FUSION PLASMA BY USING ICF METHOD

2008 ◽  
Vol 17 (06) ◽  
pp. 1131-1139
Author(s):  
S. N. HOSSEINIMOTLAGH
Keyword(s):  
Laplace Transform ◽  
Analytical Solutions ◽  
Initial Conditions ◽  
Fusion Reaction ◽  
Main Tool ◽  
Fusion Plasma ◽  
Arbitrary Boundary ◽  
One Dimensional ◽  
Special Cases ◽  
Laplace Transform Technique

Brajinskii's equations are the fundamental relations governing the behavior of the plasma produced during a fusion reaction, especially ICF plasma. These equations contains six partial differentials coupled together. In this paper we have tried to give analytical solutions to these equations using a one-dimensional method. Laplace transform technique is the main tool to do that with an arbitrary boundary and initial conditions for some special cases.

Analytical versus numerical solutions of the nonlinear fractional time–space telegraph equation

2021 ◽  
pp. 2150324
Author(s):  
Mostafa M. A. Khater ◽  
Dianchen Lu
Keyword(s):  
Analytical Solutions ◽  
Electromagnetic Waves ◽  
Numerical Scheme ◽  
Numerical Solutions ◽  
Telegraph Equation ◽  
Scatter Matrix ◽  
B Spline ◽  
Stable Property ◽  
Time Space ◽  
Matrix Distribution

In this paper, the stable analytical solutions’ accuracy of the nonlinear fractional nonlinear time–space telegraph (FNLTST) equation is investigated along with applying the trigonometric-quantic-B-spline (TQBS) method. This investigation depends on using the obtained analytical solutions to get the initial and boundary conditions that allow applying the numerical scheme in an easy and smooth way. Additionally, this paper aims to investigate the accuracy of the obtained analytical solutions after checking their stable property through using the properties of the Hamiltonian system. The considered model for this study is formulated by Oliver Heaviside in 1880 to define the advanced or voltage spectrum of electrified transmission, with day-to-day distances from the electrified communication or the application of electromagnetic waves. The matching between the analytical and numerical solutions is explained by some distinct sketches such as two-dimensional, scatter matrix, distribution, spline connected, bar normal, filling with two colors plots.

Thermodiffusion with two time delays and Kernel functions

2016 ◽  
Vol 23 (2) ◽  
pp. 195-208 ◽  
Author(s):  
Ahmed S El-Karamany ◽  
Magdy A Ezzat ◽  
Alaa A El-Bary
Keyword(s):  
Laplace Transform ◽  
Kernel Functions ◽  
Transform Domain ◽  
Thermoelastic Diffusion ◽  
One Dimensional ◽  
Laplace Transform Technique ◽  
The Laplace Transform ◽  
Isotropic Elastic Medium ◽  
Time Variations ◽  
With Memory

The present work is concerned with the investigation of disturbances in a homogeneous, isotropic elastic medium with memory-dependent derivatives (MDDs). A one-dimensional problem is considered for a half-space whose surface is traction free and subjected to the effects of thermodiffusion. For treatment of time variations, the Laplace-transform technique is utilized. The theories of coupled and of generalized thermoelastic diffusion with one relaxation time follow as limit cases. A direct approach is introduced to obtain the solutions in the Laplace transform domain for different forms of kernel functions and time delay of MDDs, which can be arbitrarily chosen. Numerical inversion is carried out to obtain the distributions of the considered variables in the physical domain and illustrated graphically. Some comparisons are made and shown in figures to estimate the effects of MDD parameters on all studied fields.

Thermoelasticity When the Material Coupling Parameter Equals Unity

1965 ◽  
Vol 32 (2) ◽  
pp. 378-382 ◽  
Author(s):  
O. W. Dillon
Keyword(s):  
Laplace Transform ◽  
Constant Velocity ◽  
Coupling Parameter ◽  
Step Function ◽  
Surface Strain ◽  
Coupled Thermoelasticity ◽  
Velocity Impact ◽  
One Dimensional ◽  
Laplace Transform Technique ◽  
The Laplace Transform

Analytical solutions of three problems in coupled thermoelasticity are presented for the case when the material coupling parameter equals unity. The problems considered are: (a) Danilovskaya’s problem of a step function in temperature at the surface; (b) a step function in surface strain; and (c) constant velocity impact. Solutions are presented for the case of thin bars (one-dimensional stress) and are obtained by the Laplace-transform technique. There is great simplification in the equations when the material coupling parameter equals unity which permits the straightforward inversion of the transformed solutions. The results demonstrate significant deviations from the corresponding uncoupled solutions.

Numerical solution for the fractional-order one-dimensional telegraph equation via wavelet technique

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Kumbinarasaiah Srinivasa ◽  
Hadi Rezazadeh
Keyword(s):  
Analytical Solution ◽  
Numerical Solution ◽  
Convergence Analysis ◽  
Collocation Method ◽  
Fractional Order ◽  
Numerical Technique ◽  
Telegraph Equation ◽  
Algebraic Equations ◽  
One Dimensional ◽  
Wavelet Collocation Method

AbstractIn this article, we proposed an efficient numerical technique for the solution of fractional-order (1 + 1) dimensional telegraph equation using the Laguerre wavelet collocation method. Some examples are illustrated to inspect the efficiency of the proposed technique and convergence analysis is discussed in terms of a theorem. Here, the fractional-order telegraph equation is converted into a system of algebraic equations using the properties of the Laguerre wavelet, and solutions obtained by the proposed scheme are more accurate and they are compared with the analytical solution and other method existed in the literature.

scholarly journals Comment on “An Approximation to Solution of Space and Time Fractional Telegraph Equations by He's Variational Iteration Method”

2013 ◽  
Vol 2013 ◽  
pp. 1-2
Author(s):  
Yi-Hong Wang ◽  
Lan-Lan Huang
Keyword(s):  
Laplace Transform ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Approximate Solutions ◽  
Telegraph Equation ◽  
Variational Iteration ◽  
Space And Time ◽  
Fractional Telegraph Equation ◽  
Telegraph Equations ◽  
He’S Variational Iteration Method

The variational iteration method was applied to the time fractional telegraph equation and some variational iteration formulae were suggested in (Sevimlican, 2010). Those formulae are improved by Laplace transform from which the approximate solutions of higher accuracies can be obtained.

scholarly journals On the stability of the telegraph equation with time delay

Filomat ◽  
2020 ◽  
Vol 34 (4) ◽  
pp. 1251-1259
Author(s):  
Allaberen Ashyralyev ◽  
Deniz Agirseven ◽  
Koray Turk
Keyword(s):  
Boundary Condition ◽  
Time Delay ◽  
Test Problem ◽  
Dirichlet Boundary ◽  
Telegraph Equation ◽  
Stability Estimates ◽  
Initial Value ◽  
One Dimensional ◽  
Telegraph Equations ◽  
The Stability

In this study, the initial value problem for telegraph equations with time delay in a Hilbert space is considered. The main theorem on stability estimates for the solution of this problem is established. As a test problem, one-dimensional delay telegraph equation with the Dirichlet boundary condition is considered.

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