To numerical solution of singular perturbed equations transformed to the best argument

We consider the numerical solution of initial value problem for the system of ordinary differential singular perturbed equations. The integral curve of the problem is constructed using method of continuation with respect to a parameter. We can choose the best parameter in any step of integration process. It is found that the best argument of the Cauchy problem is the arc length of the integral curve of the problem. Transformed to the best argument Cauchy problem has a number advantages in comparison with the Cauchy problem over the usual statement [1]. The right - hand side of each transformed equation does not exceed unit. Moreover, the squared norm of the system right - hand sides is always equal to unit. Also the suggested transformation reduces the difficulties that are typical for stiff systems. The efficiency of the approach is shown on test examples.