Some Remarks on a Variational Method for Stiff Differential Equations

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2019-05Department
Ciencias y Técnicas de la Navegación, Máquinas y Motores Térmicos y Teoría de la Señal...Source
Mathematics 2019, 7, 455Abstract
We have recently proposed a variational framework for the approximation of systems
of differential equations. We associated, in a natural way, with the original problem, a certain
error functional. The discretization is based on standard descent schemes, and we can use a
variable-step implementation. The minimization problem has a unique solution, and the approach
has a global convergence. The use of our error-functional strategy was considered by other authors,
but using a completely different way to derive the discretization. Their technique was based on the
use of an integral form of the Euler equation for a related optimal control problem, combined with
an adapted version of the shooting method, and the cyclic coordinate descent method. In this note,
we illustrate and compare our strategy to theirs from a numerical point of view.