<abstract xmlns="http://www.w3.org/1999/xhtml"><p>In this study, a robust hybrid method is used as an alternative method, which is a different method from other methods for the approximate of the telegraph equation. The hybrid method is a mixture of the finite difference and differential transformation methods. Three numerical examples are solved to prove the accuracy and efficiency of the hybrid method. The reached results from these samples are shown in tables and graphs.</p></abstract>

In this study, a robust hybrid method is used as an alternative method, which is a different method from other methods for the approximate of the telegraph equation. The hybrid method is a mixture of the finite difference and differential transformation methods. Three numerical examples are solved to prove the accuracy and efficiency of the hybrid method. The reached results from these samples are shown in tables and graphs.

The Numerical Study of a Hybrid Method for Solving Telegraph Equation

Department of Mathematics, Faculty of Art and Science

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution 4.0 International License.

{"article-title":"The Numerical Study of a Hybrid Method for Solving Telegraph Equation"}

In this study, a robust hybrid method is used as an alternative method, which is a different method from other methods for the approximate of the telegraph...

x	Exact solution	Approximate solution	Error
0.0	0.980198673	0.980198673	0
0.1	1.083287067	1.083287068	0.1×10⁻⁸
0.2	1.197217363	1.197217363	0
0.3	1.323129812	1.323129813	0.1×10⁻⁸
0.4	1.462284589	1.462284590	0.1×10⁻⁸
0.5	1.616074402	1.616074403	0.1×10⁻⁸
0.6	1.786038431	1.786038431	0
0.7	1.973877732	1.973877732	0
0.8	2.181472265	2.181472265	0
0.9	2.410899706	2.410899707	0.1×10⁻⁸
1.0	2.664456242	2.664456241	0.1×10⁻⁸

The Numerical Study of a Hybrid Method for Solving Telegraph Equation

Online veröffentlicht: 31. März 2020

Seitenbereich: 293 - 302

Eingereicht: 30. Apr. 2019

Akzeptiert: 07. Juli 2019

DOI: https://doi.org/10.2478/amns.2020.1.00027

Schlüsselwörter
1D telegraph equation, approximate solution, central difference, differential transform method, finite difference method

© 2019 Derya Arslan, published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Fig. 1

Fig. 2

Fig. 3

Exact solution, approximate solution, and error values for t = 0.01

The Numerical Study of a Hybrid Method for Solving Telegraph Equation

Online veröffentlicht: 31. März 2020

Seitenbereich: 293 - 302

Eingereicht: 30. Apr. 2019

Akzeptiert: 07. Juli 2019

DOI: https://doi.org/10.2478/amns.2020.1.00027

Schlüsselwörter1D telegraph equation, approximate solution, central difference, differential transform method, finite difference method

© 2019 Derya Arslan, published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Fig. 1

Fig. 2

Fig. 3

Exact solution, approximate solution, and error values for t = 0.01

Schlüsselwörter
1D telegraph equation, approximate solution, central difference, differential transform method, finite difference method