Numerical solution error of stiff Cauchy problems on geometrically adaptive meshes

The concept of stiffness of ODE system is refined. Major difficulties arising in solution of the corresponding Cauchy problems are pointed out. Advantages of the arc length arguments are shown. Different step selection criteria are discussed and step selection formula based on curvature of the integral curve is improved. A procedure is described which allows to a) construct mesh sequence tending to a quasi-uniform one, b) obtain majorant error estimate simultaneously with the solution. Illustrative calculation examples are given.