NUMERICAL SOLUTIONS OF THE MKdV EQUATION VIA COLLOCATION FINITE ELEMENT METHOD

In this paper, we have obtained numerical solutions of the modified Korteweg-de Vries (MKdV) equation by using septic B-spline collocation finite element method. The suggested numerical algorithm is controlled by applying three test problems including; single soliton wave, interaction of two and three soliton waves. Our numerical algorithm, attributed to a Crank Nicolson approximation in time, is unconditionally stable. To control the performance of the newly applied method, the error norms L2 ,Lsonsuz and invariants I1 ,I2 ,I3, and I4 have been calculated. The obtained numerical results are compared with some of those available in the literature