Computational study of modified regularised and regularised long wave equations using trigonometric splines

Abstract

In this paper traveling wave solutions of the modified regularized and regularized long wave equations (MRLW \& RLW equations) are simulated using modified trigonometric B-spline functions in collocation method.
We validate the adaptability of the proposed method successfully by simulating single solitary wave motion, two and three solitary wave interactions. We also compute the three motion invariants numerically and these are found to be very very close with their analytical values. We also calculate $L_2$ and $L\infty$ error norms for single solitary wave motion. Stability of the method is also discussed. Convergence rate for the proposed scheme is obtained numerically with respect to space step size. Computational complexity is analysed and it is found that the developed approach gives very good results with very less computational cost. In terms of the number of arithmetic operations, the computational complexity of the proposed method is found to be linear.