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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.

MSC:

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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