Most of partial differential equation problems are the pure Neumann’s problems, which are quite complicated to solve. In this paper, we discuss the MLPG method that reducing the complexity for solving Navier-Stokes equations by constructing the new system of equations which is equivalent to the original system. In this way, the pure Neumann’s problem is transformed to the Dirichlet’s problem, which is simpler to accomplish and also gives a more accurate solution.

two field variables, MLPG method, pure Neumann’s boundary condition, Navier-Stokes equations, Poisson’s equation.