A meshless method for the numerical computation of the solution of steady Burgers-type equations

In this paper, we discuss a meshless method for solving steady Burgers-type equations with Dirichlet boundary conditions. The numerical approximation of the solution in the given domain is obtained by using thin plate spline approximation, leading to a large-scale nonlinear matrix equation. The main difficulty of the proposed method is the numerical computation of a solution of the derived nonlinear matrix equation. We will show how to combine Newtonʼs method with some matrix Krylov subspace techniques such as the global GMRES to solve these nonlinear problems. Numerical examples are given to illustrate the proposed method.