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Solution of singular equations transformed to the best argument. (English. Russian original) Zbl 0963.65089
Russ. Math. 42, No. 11, 53-60 (1998); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 1998, No. 11, 56-63 (1998).
From the introduction: We suggest a method by which the solution of the Cauchy problem for a system of differential-algebraic equations is considered from the standpoint of the method of continuation of the solution along the parameter, which allows to pose the question on the choice of the best parameter which supplies the best conditioning to the system of linear equations of the continuation. Thus, a system of linear equations of the continuation, obtained at each step of integration process, will be the best conditioned. Moreover, by virtue of the choice of argument of the problem, the error will be less sensitive to drastic changes of the solution.
65L80 Numerical methods for differential-algebraic equations
65L05 Numerical methods for initial value problems
34A09 Implicit ordinary differential equations, differential-algebraic equations
65L70 Error bounds for numerical methods for ordinary differential equations