Numerical solution of modified regularized long wave equation by using cubic trigonometric B-spline functions

In this study, the Modified Regularized Long Wave (MRLW) equation is solved numerically.  The method used for the numerical solution of MRLW equation includes the space discretization with the Galerkin finite element method based on cubic trigonometric B-spline, and also the time discretization with the Crank-Nicolson method.  We tried to obtain a more accurate method with the help of trigonometric B-spline for the numerical solution of the MRLW equation than the existing numerical methods in the first test problem.  Then, the interaction problem of the two positive solitary waves of the MRLW equation is considered, and the conservation constants are compared with the existing ones to see the correctness of the method.