Arc length method of solving Cauchy problem with guaranteed accuracy for stiff systems

Arc length method is an efficient way of solving Cauchy problem for systems of ordinary differential equations which have areas with large values of right side of equation (stiff and ill-conditioned problems). It is shown how to get asymptotically exact a posteriori error estimation using Richardson method for such calculations. Provided examples demostrate that the bigger problem stiffness or ill-conditioning is, the bigger accuracy benefit the arc length method allows to achieve. As for hyperstiff problems (which components have significantly different orders of values), it is necessary to compute with higher digits capacity and/or analytical expression for Jacobian matrix in order to get a reliable solution.