A method of algebraic adaptation (Q1571271)

The author studies the use of special coordinate transformations in the algebraic method for constructing an adaptive grid. Blending functions and intermediate transformations for an effective adaptation of grids are defined on the basis of special extending functions. As extending functions the author uses certain basic nonuniform coordinate mappings that are the solutions of equations with small parameters at the higher derivatives. The grids obtained by these transformations are well-adapted to the peculiarities of the solutions of equations with singularities and allow to obtain a numerical solution that uniformly converges to the exact one.