Numerical solution of the KdV equation by Haar wavelet method

ORUC O., bulut F., ESEN A.

PRAMANA-JOURNAL OF PHYSICS, cilt.87, sa.6, 2016 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 87 Sayı: 6
  • Basım Tarihi: 2016
  • Doi Numarası: 10.1007/s12043-016-1286-7
  • Dergi Adı: PRAMANA-JOURNAL OF PHYSICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Anahtar Kelimeler: Haar wavelet method, Taylor-Haar, KdV equation, soliton, numerical solution, TAYLOR-GALERKIN METHOD, DYNAMICS, SCHEME
  • İnönü Üniversitesi Adresli: Evet

Özet

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.