Discrete evolutions: Convergence and applications. (English) Zbl 0823.65064

A convergence result is proved for a time discrete process of the form \[ x(t + h) - x(t) = h V (h, x(t + \alpha_ 1 (t) h), \dots, x(t + \alpha_ L (t) h)), \] \(t = T + jh\), \(j = 0, \dots, \sigma(h) - 1\) under weak conditions on the function \(V\). Furthermore, the applications to minimization problems, boundary value problems and systems of nonlinear equations are discussed.


65K10 Numerical optimization and variational techniques
65H10 Numerical computation of solutions to systems of equations
65Q05 Numerical methods for functional equations (MSC2000)
93C55 Discrete-time control/observation systems
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