In the paper the adaptive grid method for numerical solution of one dimensional convection–diffusion problems is developed. The method belongs to the class of moving grid methods. For such method coordinates of the grid points x_i^ј are unknown and have to be found from equation (x^ј_i+1–x_i^ј)М_i+₁⁄₂)–(x^ј_i–x^ј_i-1)М_{i–₁⁄₂}=0. The coefficient М_i+₁⁄₂ depends on the first u’(x^j_i+₁⁄₂,t^j) and the second u˝(x^j_i+₁⁄₂,t^j) space derivatives of the original problem solution. In the paper it is suggested to find out the function М_i+₁⁄₂ from truncation error minimization of used difference scheme. The regularization for grid point time moving is discussed. The computational examples are presented.

Mathematical problems and theory of numerical methods

Degtyarev Lev Markovich,  KIAM RAS

Ivanova T. S.,  KIAM RAS