LLWM swMATH ID: 9400 Software Authors: Yin, Fukang; Song, Junqiang; Lu, Fengshun Description: 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. Homepage: http://onlinelibrary.wiley.com/doi/10.1002/mma.2834/abstract Keywords: Laplace transform; Klein-Gordon equation; nonlinear; Legendre wavelets; recursive relation; block pulse functions Related Software: Cited in: 14 Documents all top 5 Cited by 28 Authors 5 Hosseininia, Masoumeh 4 Heydari, Mohammad Hossien 3 Avazzadeh, Zakieh 3 Song, Junqiang 3 Yin, Fukang 2 Maalek Ghaini, F. M. 1 Ahmad, Imtiaz 1 Ahsan, Muhammad 1 Bao, Weimin 1 Cattani, Carlo 1 Dong, Jian 1 Gao, Wanlin 1 Gong, Chunye 1 He, Bin 1 Heydari, Mohammadhossein 1 Hussain, Iltaf 1 Kumam, Poom 1 Kumam, Wiyada 1 Li, Gang 1 Liu, Jie 1 Lu, Fengshun 1 Mei, Shuli 1 Ram Verma, Sag 1 Rayal, Ashish 1 Roohi, Reza 1 Wu, Yongwen 1 Zhang, Chenghong 1 Zhang, Lilun all top 5 Cited in 14 Serials 1 Computers & Mathematics with Applications 1 Journal of Computational Physics 1 Mathematical Methods in the Applied Sciences 1 Chaos, Solitons and Fractals 1 Journal of Computational and Applied Mathematics 1 Applied Numerical Mathematics 1 Applied Mathematical Modelling 1 Complexity 1 Abstract and Applied Analysis 1 Fractional Calculus & Applied Analysis 1 International Journal of Nonlinear Sciences and Numerical Simulation 1 International Journal of Wavelets, Multiresolution and Information Processing 1 Discrete and Continuous Dynamical Systems. Series S 1 Symmetry all top 5 Cited in 6 Fields 13 Numerical analysis (65-XX) 9 Partial differential equations (35-XX) 3 Real functions (26-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 1 Biology and other natural sciences (92-XX) 1 Systems theory; control (93-XX) Citations by Year