| In the fields of science and engineering,many problems can be described by partial differential equations,which has practical applications in partial differential equations.But it's difficult to obtain analytic solutions,or analytical expression of solution is complex.So it is the most important method to solve the differential equation by using numerical method to obtain the approximate value.In this paper,we study the initial-boundary value problems of the generalized Rosenau-Kawahara-RLW equation and Fourth-order Hyperbolic equations by using the finite difference method.At first,a two-layer high accuracy compact difference scheme for the generalized Rosenau-Kawahara-RLW?RKRLW?equation is proposed.Combining with the energy analysis method,the conservative laws in energy and mass are proved.The existence and uniqueness of the numerical solution have been shown.The difference scheme is unconditionally stable and convergent,and its numerical convergence order isO??2+h4?in the L?-norm.The reliability and validity of the numerical theory are proved by numerical experiments.Secondly,a three-layer high accuracy compact difference scheme for the generalized Rosenau-Kawahara-RLW?RKRLW?equation is proposed.Combining with the energy analysis method,the conservative laws in energy and mass are proved.The existence and uniqueness of the numerical solution have been shown.The difference scheme is unconditionally stable and convergent,and its numerical convergence order isO??2+h4?in the L?-norm.The reliability and validity of the numerical theory are proved by numerical experiments.Finally,a three-layer high accuracy compact difference scheme for Two-dimensional Fourth-order Hyperbolic equation is proposed.The existence and uniqueness of the numerical solution have been shown.The difference scheme is unconditionally stable and convergent,and its numerical convergence order is O??2+h14+h24?in the2L-norm.The reliability and validity of the numerical theory are proved by numerical experiments. |
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