Some difference algorithms for nonlinear klein-gordon equations

Asuman Zeytinoglu; Murat Sari

doi:10.1007/978-3-030-10692-8_56

Some difference algorithms for nonlinear klein-gordon equations

Asuman Zeytinoglu, Murat Sari^*

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

1 Citation (Scopus)

Abstract

In this study, sixth and eighth-order finite difference schemes combined with a third-order strong stability preserving Runge-Kutta (SSP-RK3) method are employed to cope with the nonlinear Klein-Gordon equation, which is one of the important mathematical models in quantum mechanics, without any linearization or transformation. Various numerical experiments are examined to verify the applicability and efficiency of the proposed schemes. The results indicate that the corresponding schemes are seen to be reliable and effectively applicable. Another salient feature of these algorithms is that they achieve high-order accuracy with relatively less number of grid points. Therefore, these schemes are realized to be a good option in dealing with similar processes represented by partial differential equations.

Original language	English
Title of host publication	Numerical Methods and Applications - 9th International Conference, NMA 2018, Revised Selected Papers
Editors	Geno Nikolov, Natalia Kolkovska, Krassimir Georgiev
Publisher	Springer Verlag
Pages	491-498
Number of pages	8
ISBN (Print)	9783030106911
DOIs	https://doi.org/10.1007/978-3-030-10692-8_56
Publication status	Published - 2019
Externally published	Yes
Event	9th International conference on Numerical Methods and Applications, NMA 2018 - Borovets, Bulgaria Duration: 20 Aug 2018 → 24 Aug 2018

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	11189 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	9th International conference on Numerical Methods and Applications, NMA 2018
Country/Territory	Bulgaria
City	Borovets
Period	20/08/18 → 24/08/18

Bibliographical note

Publisher Copyright:
© Springer Nature Switzerland AG 2019.

Keywords

High-order finite difference scheme
Klein-Gordon equation
Nonlinear processes
Strong stability preserving Runge-Kutta

Access to Document

10.1007/978-3-030-10692-8_56

Cite this

Zeytinoglu, A., & Sari, M. (2019). Some difference algorithms for nonlinear klein-gordon equations. In G. Nikolov, N. Kolkovska, & K. Georgiev (Eds.), Numerical Methods and Applications - 9th International Conference, NMA 2018, Revised Selected Papers (pp. 491-498). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11189 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-030-10692-8_56

Zeytinoglu, Asuman ; Sari, Murat. / Some difference algorithms for nonlinear klein-gordon equations. Numerical Methods and Applications - 9th International Conference, NMA 2018, Revised Selected Papers. editor / Geno Nikolov ; Natalia Kolkovska ; Krassimir Georgiev. Springer Verlag, 2019. pp. 491-498 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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Zeytinoglu, A & Sari, M 2019, Some difference algorithms for nonlinear klein-gordon equations. in G Nikolov, N Kolkovska & K Georgiev (eds), Numerical Methods and Applications - 9th International Conference, NMA 2018, Revised Selected Papers. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 11189 LNCS, Springer Verlag, pp. 491-498, 9th International conference on Numerical Methods and Applications, NMA 2018, Borovets, Bulgaria, 20/08/18. https://doi.org/10.1007/978-3-030-10692-8_56

Some difference algorithms for nonlinear klein-gordon equations. / Zeytinoglu, Asuman; Sari, Murat.
Numerical Methods and Applications - 9th International Conference, NMA 2018, Revised Selected Papers. ed. / Geno Nikolov; Natalia Kolkovska; Krassimir Georgiev. Springer Verlag, 2019. p. 491-498 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11189 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AU - Zeytinoglu, Asuman

AU - Sari, Murat

N1 - Publisher Copyright: © Springer Nature Switzerland AG 2019.

PY - 2019

Y1 - 2019

N2 - In this study, sixth and eighth-order finite difference schemes combined with a third-order strong stability preserving Runge-Kutta (SSP-RK3) method are employed to cope with the nonlinear Klein-Gordon equation, which is one of the important mathematical models in quantum mechanics, without any linearization or transformation. Various numerical experiments are examined to verify the applicability and efficiency of the proposed schemes. The results indicate that the corresponding schemes are seen to be reliable and effectively applicable. Another salient feature of these algorithms is that they achieve high-order accuracy with relatively less number of grid points. Therefore, these schemes are realized to be a good option in dealing with similar processes represented by partial differential equations.

AB - In this study, sixth and eighth-order finite difference schemes combined with a third-order strong stability preserving Runge-Kutta (SSP-RK3) method are employed to cope with the nonlinear Klein-Gordon equation, which is one of the important mathematical models in quantum mechanics, without any linearization or transformation. Various numerical experiments are examined to verify the applicability and efficiency of the proposed schemes. The results indicate that the corresponding schemes are seen to be reliable and effectively applicable. Another salient feature of these algorithms is that they achieve high-order accuracy with relatively less number of grid points. Therefore, these schemes are realized to be a good option in dealing with similar processes represented by partial differential equations.

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Zeytinoglu A, Sari M. Some difference algorithms for nonlinear klein-gordon equations. In Nikolov G, Kolkovska N, Georgiev K, editors, Numerical Methods and Applications - 9th International Conference, NMA 2018, Revised Selected Papers. Springer Verlag. 2019. p. 491-498. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-030-10692-8_56

Some difference algorithms for nonlinear klein-gordon equations

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