Some Studies On The Finite Difference Methods For The Generalized Rosenau-Kawahara Equation

As wave equation is an important type of partial differential equation,hence,studies of numerical methods for wave equations undoubtedly are of important theoretical and practical significance.Among numerous numerical methods for solving wave equation,finite difference method has tremendous applications in scientific researches and engineering calculation,for it has a few characteristic virtues,for example,the convenience for coding,the simple of design scheme,the more mature of theory.In this paper,The numerical solution for a type of generalized Rosenau-Kawahara equation is considered.Two different nonlinear schemes and a linear three-level conservation finite difference scheme with second-order are respectively designed.Those finite difference schemes simulate conservation properties of the problem well.The existence and uniqueness of those finite differences solution are also obtained.It is proved that those finite differences scheme is convergent and unconditionally stable by discrete functional analysis method.The results attained form numerical experiments.