Article
MSC:
65H10,
65K10,
65L20,
65L99,
65Q05,
93C55 | MR 1228508 | Zbl 0823.65064 | DOI: 10.21136/AM.1993.104555
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Keywords:
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
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
Summary:
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.
References:
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