Application of the collocation method with b – spline to the GRLW equation

  TẠP CHÍ KHOA HỌC  SỐ 20/2017 15 APPLICATION OF THE COLLOCATION METHOD WITH B – SPLINE TO THE GRLW EQUATION Nguyen Thi Thu Hoa, Nguyen Thi Thu Ha Hanoi Metropolitan University Abstract: In this work, solitary – wave solution of the generalized regularized long wave (GRLW) equation are obtained by using quintic B – spline collocation method A linear new method based on collocation of quintic B – splines Applying the von – Neumann stability analysis of the numerical scheme base on the von Neumann method is investigate We compute the error in the and the norms and in the variants , and of the GRLW equation The numerical result are tabulated and are ploted at different time levels Keywords: Catot, LiNixMn2-xO4, pin liti-ion, LiBs Email: hoantt@daihocthudo.edu.vn  Received 05 December 2017  Accepted for publication 25 December 2017  INTRODUCTION In this work, we consider the solution of the mGRLW equation  u + αu + εu u − βu = 0,                                   (1)  where p is a positive interger number, ε, α and β are positive constants, x ∈ [a, b], t ∈ [0, T],  and the boundary and initial conditions are assumed to be of the form       u(a, t) = 0, u(b, t) = 0, u (a, t) = u (a, t) = u (a, t) = u (b, t) = 0,                                  (2)  u(x, 0) = f(x), x ∈ [a, b] The numerical solution of the GRLW has been stadied in the recent years. The septic B  – spline collocation  method  was  applied to  the GRLW  by S. BattalGaziKarakoỗa andH. Zeybek[2].RoshanhassolvedtheequationbyusingthePetrovGalerkinmethod[16] Inthispaper,aquinticB-splinecollocationmethodispresentedfortheGRLWequation. Thisworkisdesignedasfollow:inSection2,discriptionofquinticBsplinecollocation methodispresented.ThestabilityanalysisofthemethodisestablishedinSection3.InSection 4,thenumericalresultsarediscussed.InthelastSection,Section5,conclusionispresented. 16   TRƯỜNG ĐẠI HỌC THỦ ĐÔ HÀ NỘI DISCRIPTION OF QUINTIC B – SPLINE COLLOCATION METHOD We partition the interval [ , ] into elements of uniforms length h by the knots x such  that partitioned in to a mesh of uniform length by the knots x , m = 0, N such that  a=x