Uniform algorithm for computation of discontinuous solution on adaptive grids

The numerical method for computation of model transfer equation ${\partial u}/{\partial t}+{\partial u}/{\partial x}=0$ on solution-adaptive grids is presented. The adaptation of grid is based on method of equidistribution weight function. The corresponding choice of weight function and the use of high order monotonous scheme allows to receive second accuracy order both for discontinuous and for smooth solutions.