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- Title
On the sparse multiscale representation of 2‐D Burgers equations by an efficient algorithm based on multiwavelets.
- Authors
Nemati Saray, Behzad; Lakestani, Mehrdad; Dehghan, Mehdi
- Abstract
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.
- Subjects
GALERKIN methods; ALGEBRAIC equations; BURGERS' equation; HAMBURGERS; SPARSE approximations; ALGORITHMS
- Publication
Numerical Methods for Partial Differential Equations, 2023, Vol 39, Issue 3, p1938
- ISSN
0749-159X
- Publication type
Article
- DOI
10.1002/num.22795