Exponential B-spline collocation method for numerical solution of the generalized regularized long wave equation

摘要: The aim of the present paper is to a numerical algorithm for time-dependent generalized regularized long wave equation with boundary conditions. We semi-discretize continuous problem by means Crank-Nicolson finite difference method in temporal direction and exponential B-spline collocation spatial direction. shown be unconditionally stable. It that convergent an order O(k 2 +h ). Our scheme leads tri-diagonal nonlinear system. This new has lower computational cost comparison Sinc-collocation method. Finally, examples demonstrate stability accuracy this Nonlinear partial differential equations are useful describing various phenomena applied mathematics physics. Analytical solutions these usually not available, especially when terms in- volved. Since only limited classes solved analytical means, practical importance (see Refs. (1)-(5)). Solitary waves packets or pulses, which propagate dispersive media. Due dy- namical balance between nonlinearity effects, retain stable waveform. A soliton very special type solitary wave, propagates without any change its shape velocity properties after collisions other solitons. work concerned solution (RLW) equa- tion, was first derived Peregrine define undular bore development. (6) then, been used model large number problems arising ar- eas science. RLW alternative description more usual Korteweg-de Vries (KdV) equation. found have govern impor- tant physical such as transverse shallow water, ion-acoustic, magneto-hydrodynamic plasma phonon crystals, anhar- monic lattices, longitudinal elastic rods, pressure liquid-gas bubble mixtures, rotating flow down tube, lossless propagation water waves, thermally exited low-temperature crystals. (7-9) Indeed, case (GRLW) given