On the sparse multiscale representation of <scp>2‐D</scp> Burgers equations by an efficient algorithm based on multiwavelets
Behzad Nemati Saray, Mehrdad Lakestani, Mehdi Dehghan
Abstract
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 L 2 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.