A new approach for the numerical solution for nonlinear Klein–Gordon equation


In this article, we generated a new operational matrix of integration using Clique polynomials of complete graphs and also introducing a new numerical technique to solve nonlinear Klein–Gordon equation. These equations describe a variety of physical phenomena such as ferroelectric and ferromagnetic domain walls, and DNA dynamics. We obtain an approximate solution for the nonlinear Klein–Gordon equation using the present method by transforming a system of nonlinear algebraic equations. The proposed scheme is applied to some examples and compared with another method in the literature that demonstrates the effectiveness of this method.

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The author wish to express his thanks to Karnatak University and Bangalore University for the necessary support.

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Correspondence to S. Kumbinarasaiah.

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Kumbinarasaiah, S. A new approach for the numerical solution for nonlinear Klein–Gordon equation. SeMA (2020). https://doi.org/10.1007/s40324-020-00225-y

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  • Operational matrix
  • Partial differential equations
  • Collocation method
  • Clique polynomials

Mathematics Subject Classification

  • 35-XX
  • 65M70
  • 05Cxx