An efficient Strang splitting technique combined with the multiquadric-radial basis function for the Burgers' equation

SEYDAOĞLU M., UÇAR Y., KUTLUAY S.

COMPUTATIONAL & APPLIED MATHEMATICS, cilt.40, sa.8, 2021 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 40 Sayı: 8
  • Basım Tarihi: 2021
  • Doi Numarası: 10.1007/s40314-021-01692-3
  • Dergi Adı: COMPUTATIONAL & APPLIED MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Applied Science & Technology Source, Computer & Applied Sciences, zbMATH
  • Anahtar Kelimeler: Burgers' equation, Strang splitting, Multiquadric-radial basis function, DATA APPROXIMATION SCHEME, FINITE-DIFFERENCE SCHEME, NUMERICAL-SOLUTION, MESHLESS METHOD, RBF, ELEMENT, ALGORITHM, IMPLICIT
  • İnönü Üniversitesi Adresli: Evet

Özet

In the present paper, two effective numerical schemes depending on a second-order Strang splitting technique are presented to obtain approximate solutions of the one-dimensional Burgers' equation utilizing the collocation technique and approximating directly the solution by multiquadric-radial basis function (MQ-RBF) method. To show the performance of both schemes, we have considered two examples of Burgers' equation. The obtained numerical results are compared with the available exact values and also those of other publishedmethods. Moreover, the computed L-2 and L-infinity error norms have been given. It is found that the presented schemes produce better results as compared to those obtained almost all the schemes present in the literature.