Discrete evolutions: Convergence and applications

Erich Bohl; Johannes Schropp

Applications of Mathematics (1993)

  • Volume: 38, Issue: 4-5, page 266-280
  • ISSN: 0862-7940

Abstract

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We prove a convergence result for a time discrete process of the form x ( t + h ) - x ( t ) = h V ( h , x ( t + α 1 ( t ) h ) , . . . , x ( t + α L ( t ) h ) ) t = T + j h , j = 0 , . . . , σ ( 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.

How to cite

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Bohl, Erich, and Schropp, Johannes. "Discrete evolutions: Convergence and applications." Applications of Mathematics 38.4-5 (1993): 266-280. <http://eudml.org/doc/15754>.

@article{Bohl1993,
abstract = {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.},
author = {Bohl, Erich, Schropp, Johannes},
journal = {Applications of Mathematics},
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 evolutions; convergence; time discrete process; systems of nonlinear equations},
language = {eng},
number = {4-5},
pages = {266-280},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Discrete evolutions: Convergence and applications},
url = {http://eudml.org/doc/15754},
volume = {38},
year = {1993},
}

TY - JOUR
AU - Bohl, Erich
AU - Schropp, Johannes
TI - Discrete evolutions: Convergence and applications
JO - Applications of Mathematics
PY - 1993
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 38
IS - 4-5
SP - 266
EP - 280
AB - 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.
LA - eng
KW - 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 evolutions; convergence; time discrete process; systems of nonlinear equations
UR - http://eudml.org/doc/15754
ER -

References

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