Generalized Rosenau- RLW equation in B-spline scheme via BFRK approach

Archana Senapati; Saumya Ranjan Jena

Archana Senapati School of Applied Sciences, KIIT Deemed to be University,\\Bhubenaswar-750124, Odisha, India.
Saumya Ranjan Jena School of Applied Sciences, KIIT Deemed to be University,\\Bhubenaswar-750124, Odisha, India.

Abstract

In this work, a septic B-spline scheme is used to simplify the process of solving an approximate solution of the generalized Rosenau-regularized long wave equation (GR-RLWE) with initial-boundary conditions. The resulting system of first order ODEs are dealt with Butcher\textsc{\char13}s fifth order Runge-Kutta (BFRK) approach without using finite difference techniques for discretizing the time dependent variables at each time level. Here no transformation or any kind of linearization technique is employed to tackle the non linearity of the equation.Two test problems are selected and compared with other researchers on the basis of efficiency, accuracy and results of the two invariants $M_I$ (mass) and $ E_I$ (energy) of some motion are used to test the conservative properties of the proposed scheme.