LLWM
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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References in zbMATH (referenced in 12 articles )
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- Hariharan, G.; Kannan, K.: Review of wavelet methods for the solution of reaction-diffusion problems in science and engineering (2014)
- Yin, Fukang; Song, Junqiang; Lu, Fengshun: A coupled method of Laplace transform and Legendre wavelets for nonlinear Klein-Gordon equations (2014)
- 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)