Collocation method using quadratic B-spline for the RLW equation

Abstract

A Collocation method is presented here for the Regularized Long Wave (RLW) equation by using Quadratic B-splines at mid points as element shape functions. A linear stability analysis shows the scheme to be unconditionally stable. Test problems, including the migration and interaction of solitary waves, are used to validate the method which is found to be accurate and efficient. The three invariants of the motion are evaluated to determine the conservation properties of the algorithm. The temporal evaluation of a Maxwellian initial pulse is then studied, and then we prove that the number of solitons which are generated from Maxwellian initial conditions are determined and we compare our results with earlier studies.

Keywords:

• RLW
• Quadratic B-spline
• Collocation
• Nonlinear PDE

C.R. Categories:

• G1.8

^∗Corresponding author.

^∗Corresponding author.

Notes

^∗Corresponding author.