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discrete processes; continuous processes; convergence of discretisations; boundary value problems; minimizing problems; Newton's iteration and Newton's flow; discrete evolutions; systems of nonlinear equations
We prove a convergence result for a time discrete process of the form $x(t+h)-x(t)=hV(h,x(t+\alpha_1(t)h), ..., x(t+\alpha_L(t)h)) t=T+jh, j=0, ..., \sigma(h)-1$ under weak conditions on the function $V$. This result is a slight generalization of the convergence result given in [5].Furthermore, we discuss applications to minimizing problems, boundary value problems and systems of nonlinear equations.
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