Baleanu, DumitruDoha, Eid HassanBhrawy, Ali H.Baleanu, DumitruAbdelkawy, M. A.2020-12-102020-12-102014Doha, 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/20.500.12416/4329A semi-analytical solution based on a Jacobi-Gauss-Lobatto collocation (J-GLC) 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-Nyström scheme. Numerical results show that the proposed algorithm is efficient, accurate, and compare favorably with the analytical solutions.eninfo:eu-repo/semantics/closedAccessJacobi Collocation MethodJacobi-Gauss-Lobatto QuadratureNonlinear Coupled HyperbolicKlein-Gordon EquationsNonlinear PhenomenaArticle593-4247264