On the sparse multiscale representation of 2-D Burgers equations by an efficient algorithm based on multiwavelets

Nemati Saray B., Lakestanı M., Dehghan M.

Numerical Methods for Partial Differential Equations, cilt.39, sa.3, ss.1938-1961, 2023 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 39 Sayı: 3
  • Basım Tarihi: 2023
  • Doi Numarası: 10.1002/num.22795
  • Dergi Adı: Numerical Methods for Partial Differential Equations
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, Compendex, MathSciNet, zbMATH, DIALNET, Civil Engineering Abstracts
  • Sayfa Sayıları: ss.1938-1961
  • Anahtar Kelimeler: Burgers equation, energy method, multiwavelets, wavelet Galerkin method
  • Van Yüzüncü Yıl Üniversitesi Adresli: Evet

Özet

In this work, we design, analyze, and test the multiwavelets Galerkin method to solve the two-dimensional Burgers equation. Using Crank–Nicolson scheme, time is discretized and a PDE is obtained for each time step. We use the multiwavelets Galerkin method for solving these PDEs. Multiwavelets Galerkin method reduces these PDEs to sparse systems of algebraic equations. The cost of this method is proportional to the number of nonzero coefficients at each time step. The results illustrate, by selecting the appropriate threshold while the number of nonzero coefficients reduces, the error will not be less than a certain amount. The L2 stability and convergence of the scheme have been investigated by the energy method. Illustrative examples are provided to verify the efficiency and applicability of the proposed method.