Study of One Dimensional Hyperbolic Telegraph Equation Via a Hybrid Cubic B-Spline Differential Quadrature Method

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Brajesh Kumar Singh ◽  
Jai Prakash Shukla ◽  
Mukesh Gupta
Keyword(s):  
Differential Quadrature Method ◽  
Telegraph Equation ◽  
Differential Quadrature ◽  
Quadrature Method ◽  
B Spline ◽  
One Dimensional

A new perspective for the numerical solutions of the cmKdV equation via modified cubic B-spline differential quadrature method

2018 ◽  
Vol 29 (06) ◽  
pp. 1850043 ◽  
Author(s):  
Ali Başhan ◽  
N. Murat Yağmurlu ◽  
Yusuf Uçar ◽  
Alaattin Esen
Keyword(s):  
Solitary Wave ◽  
Solitary Waves ◽  
Numerical Solutions ◽  
Differential Quadrature Method ◽  
Differential Quadrature ◽  
Present Approach ◽  
Test Problems ◽  
Quadrature Method ◽  
Error Norm ◽  
B Spline

In the present paper, a novel perspective fundamentally focused on the differential quadrature method using modified cubic B-spline basis functions are going to be applied for obtaining the numerical solutions of the complex modified Korteweg–de Vries (cmKdV) equation. In order to test the effectiveness and efficiency of the present approach, three test problems, that is single solitary wave, interaction of two solitary waves and interaction of three solitary waves will be handled. Furthermore, the maximum error norm [Formula: see text] will be calculated for single solitary wave solutions to measure the efficiency and the accuracy of the present approach. Meanwhile, the three lowest conservation quantities will be calculated and also used to test the efficiency of the method. In addition to these test tools, relative changes of the invariants will be calculated and presented. In the end of these processes, those newly obtained numerical results will be compared with those of some of the published papers. As a conclusion, it can be said that the present approach is an effective and efficient one for solving the cmKdV equation and can also be used for numerical solutions of other problems.

scholarly journals Differential Quadrature Solution of Hyperbolic Telegraph Equation

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
B. Pekmen ◽  
M. Tezer-Sezgin
Keyword(s):  
Numerical Solution ◽  
Good Accuracy ◽  
Differential Quadrature Method ◽  
Telegraph Equation ◽  
Differential Quadrature ◽  
Time Interval ◽  
Quadrature Method ◽  
Time Level ◽  
Time Direction ◽  
Grid Points

Differential quadrature method (DQM) is proposed for the numerical solution of one- and two-space dimensional hyperbolic telegraph equation subject to appropriate initial and boundary conditions. Both polynomial-based differential quadrature (PDQ) and Fourier-based differential quadrature (FDQ) are used in space directions while PDQ is made use of in time direction. Numerical solution is obtained by using Gauss-Chebyshev-Lobatto grid points in space intervals and equally spaced and/or GCL grid points for the time interval. DQM in time direction gives the solution directly at a required time level or steady state without the need of iteration. DQM also has the advantage of giving quite good accuracy with considerably small number of discretization points both in space and time direction.

Sign in / Sign up

Export Citation Format

Share Document