A coupled method of Laplace transform and Legendre wavelets for nonlinear Klein-Gordon equations. Klein-Gordon equation models many phenomena in both physics and applied mathematics. In this paper, a coupled method of Laplace transform and Legendre wavelets, named (LLWM), is presented for the approximate solutions of nonlinear Klein-Gordon equations. By employing Laplace operator and Legendre wavelets operational matrices, the Klein-Gordon equation is converted into an algebraic system. Hence, the unknown Legendre wavelets coefficients are calculated in the form of series whose components are computed by applying a recursive relation. Block pulse functions are used to calculate the Legendre wavelets coefficient vectors of nonlinear terms. The convergence analysis of the LLWM is discussed. The results show that LLWM is very effective and easy to implement.

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  1. Ahmad, Imtiaz; Ahsan, Muhammad; Hussain, Iltaf; Kumam, Poom; Kumam, Wiyada: Numerical simulation of PDEs by local meshless differential quadrature collocation method (2019)
  2. Dong, Jian; He, Bin; Zhang, Chenghong; Li, Gang: Open-closed-loop PD iterative learning control with a variable forgetting factor for a two-wheeled self-balancing mobile robot (2019)
  3. Hosseininia, M.; Heydari, M. H.: Legendre wavelets for the numerical solution of nonlinear variable-order time fractional 2D reaction-diffusion equation involving Mittag-Leffler non-singular kernel (2019)
  4. Hosseininia, M.; Heydari, M. H.; Maalek Ghaini, F. M.; Avazzadeh, Z.: A wavelet method to solve nonlinear variable-order time fractional 2D Klein-Gordon equation (2019)
  5. Hosseininia, M.; Heydari, M. H.; Roohi, R.; Avazzadeh, Z.: A computational wavelet method for variable-order fractional model of dual phase lag bioheat equation (2019)
  6. Hosseininia, M.; Heydari, M. H.; Avazzadeh, Z.; Maalek Ghaini, F. M.: Two-dimensional Legendre wavelets for solving variable-order fractional nonlinear advection-diffusion equation with variable coefficients (2018)
  7. Mei, Shuli; Gao, Wanlin: Shannon-Cosine wavelet spectral method for solving fractional Fokker-Planck equations (2018)
  8. Gong, Chunye; Bao, Weimin; Liu, Jie: A piecewise memory principle for fractional derivatives (2017)
  9. Yin, Fukang; Tian, Tian; Song, Junqiang; Zhu, Min: Spectral methods using Legendre wavelets for nonlinear Klein/sine-Gordon equations (2015)
  10. Hariharan, G.; Kannan, K.: Review of wavelet methods for the solution of reaction-diffusion problems in science and engineering (2014)
  11. Yin, Fukang; Song, Junqiang; Lu, Fengshun: A coupled method of Laplace transform and Legendre wavelets for nonlinear Klein-Gordon equations (2014)
  12. Yin, Fukang; Song, Junqiang; Wu, Yongwen; Zhang, Lilun: Numerical solution of the fractional partial differential equations by the two-dimensional fractional-order Legendre functions (2013)