Some difference algorithms for nonlinear klein-gordon equations

Asuman Zeytinoglu, Murat Sari*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

1 Citation (Scopus)


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 languageEnglish
Title of host publicationNumerical Methods and Applications - 9th International Conference, NMA 2018, Revised Selected Papers
EditorsGeno Nikolov, Natalia Kolkovska, Krassimir Georgiev
PublisherSpringer Verlag
Number of pages8
ISBN (Print)9783030106911
Publication statusPublished - 2019
Externally publishedYes
Event9th International conference on Numerical Methods and Applications, NMA 2018 - Borovets, Bulgaria
Duration: 20 Aug 201824 Aug 2018

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume11189 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference9th International conference on Numerical Methods and Applications, NMA 2018

Bibliographical note

Publisher Copyright:
© Springer Nature Switzerland AG 2019.


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


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