Doha, E. H.Baleanu, DumitruBhrawy, A. H.Baleanu, D.Abdelkawy, M. A.Matematik2025-09-232025-09-232014Doha, Eid Hassan... et al. (2014). "Numerical treatment of coupled nonlinear hyperbolic Klein-Gordon equations", Romanian Journal of Physics, Vol. 59, No. 3-4, pp. 247-264.1221-146Xhttps://hdl.handle.net/20.500.12416/15642Abdelkawy, Mohamed/0000-0002-9043-9644; Doha, Eid/0000-0002-7781-6871A semi-analytical solution based on a Jacobi-Gauss-Lobatto collocation (J-GL-C) method is proposed and developed for the numerical solution of the spatial variable for two nonlinear coupled Klein-Gordon (KG) partial differential equations. The general Jacobi-Gauss-Lobatto points are used as collocation nodes in this approach. The main characteristic behind the J-GL-C approach is that it reduces such problems to solve a system of ordinary differential equations (SODEs) in time. This system is solved by diagonally-implicit Runge-Kutta-Nystrom scheme. Numerical results show that the proposed algorithm is efficient, accurate, and compare favorably with the analytical solutions.eninfo:eu-repo/semantics/closedAccessNonlinear Coupled Hyperbolic Klein-Gordon EquationsNonlinear PhenomenaJacobi Collocation MethodJacobi-Gauss-Lobatto QuadratureArticle2-s2.0-84899136681