Geodesic
Discrete evolutions: Convergence and applications
Applications of Mathematics, Tome 38 (1993) no. 4-5, pp. 266-280.

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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.
DOI : 10.21136/AM.1993.104555
Classification : 65H10, 65K10, 65L20, 65L99, 65Q05, 93C55
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 
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     title = {Discrete evolutions: {Convergence} and applications},
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Bohl, Erich; Schropp, Johannes. Discrete evolutions: Convergence and applications. Applications of Mathematics, Tome 38 (1993) no. 4-5, pp. 266-280. doi : 10.21136/AM.1993.104555. http://geodesic.mathdoc.fr/articles/10.21136/AM.1993.104555/

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