Solution of differential-algebraic equations with the choice of the best argument (Q1975799)

The authors examine the problem of numerically solving the Cauchy problem for a system of differential-algebraic equations in the framework of the method of continuation with respect to a parameter. Such an approach brings one to the problem of choosing the parameter of the solution continuation that ensures the best conditionality of a set of linear continuation equations and allows to transform the original problem to that with the best argument, which is the length of an arc of the integral curve. The efficiency of the suggested transformation is illustrated by several examples.