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^*

^*Bu çalışma için yazışmadan sorumlu yazar

Araştırma sonucu: ???type-name??? › Konferans katkısı › bilirkişi

1 Atıf (Scopus)

Özet

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.

Orijinal dil	İngilizce
Ana bilgisayar yayını başlığı	Numerical Methods and Applications - 9th International Conference, NMA 2018, Revised Selected Papers
Editörler	Geno Nikolov, Natalia Kolkovska, Krassimir Georgiev
Yayınlayan	Springer Verlag
Sayfalar	491-498
Sayfa sayısı	8
ISBN (Basılı)	9783030106911
DOI'lar	https://doi.org/10.1007/978-3-030-10692-8_56
Yayın durumu	Yayınlandı - 2019
Harici olarak yayınlandı	Evet
Etkinlik	9th International conference on Numerical Methods and Applications, NMA 2018 - Borovets, Bulgaria Süre: 20 Ağu 2018 → 24 Ağu 2018

Yayın serisi

Adı	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Hacim	11189 LNCS
ISSN (Basılı)	0302-9743
ISSN (Elektronik)	1611-3349

???event.eventtypes.event.conference???

???event.eventtypes.event.conference???	9th International conference on Numerical Methods and Applications, NMA 2018
Ülke/Bölge	Bulgaria
Şehir	Borovets
Periyot	20/08/18 → 24/08/18

Bibliyografik not

Publisher Copyright:
© Springer Nature Switzerland AG 2019.

Belgeye Erişim

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

Diğer Dosyalar ve Linkler

Link to publication in Scopus

Alıntı Yap

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); Hac. 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. editör / 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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title = "Some difference algorithms for nonlinear klein-gordon equations",

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.",

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

author = "Asuman Zeytinoglu and Murat Sari",

note = "Publisher Copyright: {\textcopyright} Springer Nature Switzerland AG 2019.; 9th International conference on Numerical Methods and Applications, NMA 2018 ; Conference date: 20-08-2018 Through 24-08-2018",

year = "2019",

doi = "10.1007/978-3-030-10692-8_56",

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series = "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), hac. 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); Hac. 11189 LNCS).

Araştırma sonucu: ???type-name??? › Konferans katkısı › bilirkişi

TY - GEN

T1 - Some difference algorithms for nonlinear klein-gordon equations

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.

KW - High-order finite difference scheme

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KW - Nonlinear processes

KW - Strong stability preserving Runge-Kutta

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Zeytinoglu A, Sari M. Some difference algorithms for nonlinear klein-gordon equations. In Nikolov G, Kolkovska N, Georgiev K, editörler, 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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