Numerical solution of the KdV equation by Haar wavelet method


ORUC O., bulut F., ESEN A.

PRAMANA-JOURNAL OF PHYSICS, vol.87, no.6, 2016 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 87 Issue: 6
  • Publication Date: 2016
  • Doi Number: 10.1007/s12043-016-1286-7
  • Journal Name: PRAMANA-JOURNAL OF PHYSICS
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Keywords: Haar wavelet method, Taylor-Haar, KdV equation, soliton, numerical solution, TAYLOR-GALERKIN METHOD, DYNAMICS, SCHEME

Abstract

This paper aims to get numerical solutions of one-dimensional KdV equation by Haar wavelet method in which temporal variable is expanded by Taylor series and spatial variables are expanded with Haar wavelets. The performance of the proposed method is measured by four different problems. The obtained numerical results are compared with the exact solutions and numerical results produced by other methods in the literature. The comparison of the results indicate that the proposed method not only gives satisfactory results but also do not need large amount of CPU time. Error analysis of the proposed method is also investigated.

This paper aims to get numerical solutions of one-dimensional KdV equation by Haar wavelet method in which temporal variable is expanded by Taylor series and spatial variables are expanded with Haar wavelets. The performance of the proposed method is measured by four different problems. The obtained numerical results are compared with the exact solutions and numerical results produced by other methods in the literature. The comparison of the results indicate that the proposed method not only gives satisfactory results but also do not need large amount of CPU time. Error analysis of the proposed method is also investigated.