Solitary Wave Formation from a Generalized Rosenau Equation

Table 2

Examples of generalized Rosenau equations = 0, their acronyms, and numerical methods for their solution.

E.A.		Numerical method
R		dGM () [15]
R		CN, iterative SOR FDM [22]
R		Conservative IL3TL FDM [23]
R		EB Galerkin FEM [24]
R		Conservative IL3TL FDM [25]
R		Conservative IL3TL FDM [26]
R-B		Conservative IL3TL FDM [27]
R-B		Conservative IL3TL FDM [28]
R-B		CN FDM [29]
R-B		RK3 QBSPCM [30]
R-B		Conservative IL3TL FDM [31]
R-B		Implicit IL2TL FDM [32]
R-B		Conservative IL3TL FDM [33]
R-KdV		Conservative IL3TL FDM [34]
R-KdV		RK3 QBSPCM [35]
R-KdV		Conservative IL3TL FDM [36]
R-KdV		Conservative CN FDM [37]
R-KdV		EB FEM [38]
R-KdV		CN FEM [38]
R-KdV		IL3TL FEM [38]
R-RLW		Conservative IL2TL FDM [39]
R-RLW		Conservative IL3TL FDM [40]
R-RLW		Galerkin FEM with CN [41]
R-RLW		Conservative CN FDM [42]
R-RLW		IL3TL FDM [43]
R-RLW		RK54 QBSPCM [44]
R-RLW		Conservative IL3TL FDM [36]
R-KdV-RLW		Conservative IL3TL FDM [36]

Equation acronym (E.A.): R = Rosenau, RLW = regularized long-wave, B = Burgers, and KdV = Korteweg-de Vries. Numerical method: dGM = discontinuous Galerkin method, FDM = finite difference method, FEM = finite element method, QBSPCM = quintic B-splines collocation method, SOR = successive overrelaxation, CN = Crank-Nicolson, RK3 = third-order accurate Runge-Kutta method, IL2TL = implicit linear two-time level, IL3TL = implicit linear three-time level, and EB = Euler's backward time discretization. Unless stated otherwise θ = 1.