Some Difference Algorithms for Nonlinear Klein-Gordon Equations


in: Lecture Notes in Computer Science book series (LNCS, volume 11189) - Numerical Methods and Applications, Nikolov Geno, Kolkovska Natalia, Georgiev Krassimir, Editor, Springer, pp.491-498, 2019 identifier identifier

  • Publication Type: Book Chapter / Chapter Vocational Book
  • Publication Date: 2019
  • Doi Number: 10.1007/978-3-030-10692-8_56
  • Publisher: Springer
  • Page Numbers: pp.491-498
  • Editors: Nikolov Geno, Kolkovska Natalia, Georgiev Krassimir, Editor
  • Keywords: Klein-Gordon equation, Nonlinear processes, High-order finite difference scheme, Strong stability preserving Runge-Kutta, NUMERICAL-SOLUTION
  • Süleyman Demirel University Affiliated: Yes


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.