TẠP CHÍ KHOA HỌC SỐ 20/2017 QUARTIC B SPLINES COLLOCATION METHOD FOR NUMERICAL SOLUTION OF THE MRLW EQUATION Nguyen Van Dung1, Nguyen Viet Chinh2 Hanoi National University of Education Hanoi Metropolitan University Abstract: In this paper, numerical solutions of the modified regularized long wave (MRLW) equation are obtained by a method based on collocation of quartic B splines Applying the von-Neumann stability analysis, the proposed method is shown to be unconditionally stable The method is applied on some test examples, and the numerical results have been compared with the exact solutions The and in the solutions show the efficiency of the method computationally Keywords: MRLW equation; quartic B spline; collocation method; finite difference Email: nvdungkiev@yahoo.com Received 02 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) x ∈ [a, b], t ∈ [0, T], with the initial condition u(x, 0) = f(x), x ∈ [a, b], (2) u(a, t) = 0, u(b, t) = u (a, t) = u (a, t) = u (a, t) = u (b, t) = 0, (3) and the boundary condition where α, ε, β are constants, β > 0. TRƯỜNG ĐẠI HỌC THỦ ĐÔ HÀ NỘI The MRLW equations play a dominant role in many branches of science and engineering [1]. In the past several years, many different methods have been used to estimate the solution of the MRLW equation, for example, see [1, 3]. In this present work, we have applied the quartic B spline collocation method to the MRLW equations. This work is built as follow: in Section 2, numerical scheme is presented. Section 3, is devoted to stability analysis of the method. The numerical results are discussed in Section 4. A conclusion is given at the end of the paper in Section 5. QUINTIC B – SPLINE COLLOCATION METHOD The interval [ , ] is partitioned in to a mesh of uniform lengthh = x knots x , i = 0, N such that a=x