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

作者：Bouhamidi A; Hached M^*; Jbilou K

来源：Applied Numerical Mathematics, 2013, 74: 95-110.

DOI：10.1016/j.apnum.2013.07.004

• Viscous Burgers equation
• Meshless method
• Global GMRES
• Newton's method
• Krylov projection methods
• Radial basis functions
• Numerical analysis

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 Newton's 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.

• 出版日期2013-12