scholarly journals An efficient numerical scheme for fractional model of telegraph equation

2021 ◽  
Author(s):  
M.S. Hashmi ◽  
Urfa Aslam ◽  
Jagdev Singh ◽  
Kottakkaran Sooppy Nisar
Keyword(s):  
Numerical Scheme ◽  
Telegraph Equation ◽  
Fractional Model

Continuous symmetries of the discrete nonlinear telegraph equation

1999 ◽  
Vol 10 (3) ◽  
pp. 265-284 ◽  
Author(s):  
M. S. ODY ◽  
A. K. COMMON ◽  
M. I. SOBHY
Keyword(s):  
Initial Data ◽  
Difference Equations ◽  
Numerical Scheme ◽  
Telegraph Equation ◽  
Lie Symmetries ◽  
Discrete Equation ◽  
Symmetry Reductions ◽  
Nonlinear Telegraph Equation ◽  
Continuous Symmetries

The method of classical Lie symmetries, generalised to differential-difference equations by Quispel, Capel and Sahadevan, is applied to the discrete nonlinear telegraph equation. The symmetry reductions thus obtained are compared with analogous results for the continuous telegraph equation. Some of these ‘continuous’ reductions are used to provide initial data for a numerical scheme which attempts to solve the corresponding discrete equation.

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.

FEATURES OF SEEPAGE OF A LIQUID TO A CHINK IN THE CRACKED DEFORMABLE LAYER

2010 ◽  
Vol 01 (03) ◽  
pp. 333-347 ◽  
Author(s):  
T. S. ALEROEV ◽  
H. T. ALEROEVA ◽  
JIANFEI HUANG ◽  
NINGMING NIE ◽  
YIFA TANG ◽  
...  
Keyword(s):  
Differential Equation ◽  
Initial Value Problem ◽  
Numerical Scheme ◽  
Variable Coefficients ◽  
Initial Value ◽  
Nonlinear Fractional Differential Equation ◽  
Fractional Model ◽  
New Model ◽  
Whole Process ◽  
Fractional Differential

We establish a new model for seepage of a liquid to a chink in the cracked deformable layer, an initial value problem of nonlinear fractional differential equation with variable coefficients, then design a numerical scheme of order 2 to solve this initial value problem. This new model theoretically explains the operating thickness H of a layer depending on the values of pressure gradient on the whole chink rather than on one point, which is practiced by a large amount of data. Compared with the Dontsov equation, our fractional model considers more aspects of the whole process. The earlier rejected results can also be considered in the display lines of the fractional model.

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.

scholarly journals An efficient numerical scheme for fractional model of HIV-1 infection of CD4+ T-cells with the effect of antiviral drug therapy

2020 ◽  
Vol 59 (4) ◽  
pp. 2053-2064 ◽  
Author(s):  
Sunil Kumar ◽  
Ranbir Kumar ◽  
Jagdev Singh ◽  
K.S. Nisar ◽  
Devendra Kumar
Keyword(s):  
T Cells ◽  
Drug Therapy ◽  
Cd4 T Cells ◽  
Numerical Scheme ◽  
Antiviral Drug ◽  
Fractional Model ◽  
Hiv 1

scholarly journals A reliable numerical algorithm for a fractional model of Fitzhugh-Nagumo equation arising in the transmission of nerve impulses

2019 ◽  
Vol 8 (1) ◽  
pp. 719-727 ◽  
Author(s):  
Amit Prakash ◽  
Hardish Kaur
Keyword(s):  
Error Analysis ◽  
Laplace Transform ◽  
Perturbation Method ◽  
Numerical Algorithm ◽  
Numerical Scheme ◽  
Homotopy Perturbation Method ◽  
Fractional Model ◽  
Homotopy Perturbation ◽  
Nagumo Equation ◽  
Homotopy Polynomials

Abstract The key objective of this paper is to study the fractional model of Fitzhugh-Nagumo equation (FNE) with a reliable computationally effective numerical scheme, which is compilation of homotopy perturbation method with Laplace transform approach. Homotopy polynomials are employed to simplify the nonlinear terms. The convergence and error analysis of the proposed technique are presented. Numerical outcomes are shown graphically to prove the efficiency of proposed scheme.

NUMERICAL SCHEME OF THE WAHA CODE

2008 ◽  
Vol 20 (3-4) ◽  
pp. 323-354 ◽  
Author(s):  
Iztok Tiselj ◽  
A. Horvat ◽  
J. Gale
Keyword(s):  
Numerical Scheme
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