Journal of Applied Mathematics · 2014 · 25 citations · 20 references
Natural SciencesMathematicsComputational MechanicsComputational PhysicsDifferential EquationsBoundary-value ProblemsConvergence AnalysisDifference EquationsFinite Difference MethodsNumerical ConvergenceNumerical Methods For Differential EquationsFinite Difference DiscretizationFinite Difference SchemesFinite Difference Solution Of Partial Differential EquationsInitial Value Problem FormulationInitial-boundary Value ProblemsKdv EquationLinear Difference EquationsStability Of Finite Difference Schemes
An average linear finite difference scheme for the numerical solution of the initial-boundary value problem of Generalized Rosenau-KdV equation is proposed. The existence, uniqueness, and conservation for energy of the difference solution are proved by the discrete energy norm method. It is shown that the finite difference scheme is 2nd-order convergent and unconditionally stable. Numerical experiments verify that the theoretical results are right and the numerical method is efficient and reliable.
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Dynamics of Dense Discrete Systems: High Order Effects
Philip Rosenau · Progress of Theoretical Physics · 1988 · 205 citations · Full text
A new conservative finite difference scheme for the Rosenau equation
Khaled Omrani, Fayçal Abidi, Talha Achouri et al. · Applied Mathematics and Computation · 2007 · 100 citations