Numerical solutions of nonhomogeneous Rosenau type equations by quintic B-spline collocation method


ÖZER S. , YAĞMURLU N. M.

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2022 (Journal Indexed in SCI) identifier

  • Publication Type: Article / Article
  • Publication Date: 2022
  • Doi Number: 10.1002/mma.8125
  • Title of Journal : MATHEMATICAL METHODS IN THE APPLIED SCIENCES
  • Keywords: collocation method, quintic B-Spline functions, Rosenau, Rosenau-KdV-RLW, Rosenau-Burger, Rosenau-RLW, FINITE-DIFFERENCE SCHEME, KDV-RLW EQUATION, SHOCK-WAVES, SOLITONS

Abstract

In this study, a numerical scheme based on a collocation finite element method using quintic B-spline functions for getting approximate solutions of nonhomogeneous Rosenau type equations prescribed by initial and boundary conditions is proposed. The numerical scheme is tested on four model problems with known exact solutions. To show how accurate results the proposed scheme produces, the error norms defined by L-2 and L-infinity are calculated. Additionally, the stability analysis of the scheme is done by means of the von Neuman method.