Local method of approximate particular solutions for two-dimensional unsteady Burgers’ equations

The local method of approximate particular solutions (LMAPS) is first proposed to solve Burgers’ equations. In avoiding the ill-conditioning problem, the weight coefficients of linear combination with respect to the function values and its derivatives can be obtained by solving low-order linear systems within the local supporting domain. Then the global solutions can be obtained by reformulating the local matrix in the global and sparse matrix. The obtained large sparse linear systems are directly solved instead of using more complicated iterative method. The numerical experiments have shown that the proposed method is suitable for solving the two-dimensional unsteady Burgers’ equations with high accuracy and efficiency.