diff options
Diffstat (limited to 'mne')
| -rw-r--r-- | mne/n.lyx | 15 | ||||
| -rw-r--r-- | mne/n4.lyx | 50 |
2 files changed, 47 insertions, 18 deletions
@@ -162,6 +162,10 @@ https://en.wikipedia.org/ \lang english Runge-Kutta methods \emph default +, +\emph on +Backward Differentiation Formula +\emph default \lang spanish . \end_layout @@ -223,14 +227,10 @@ filename "n4.lyx" \end_layout \begin_layout Chapter -\begin_inset Note Note -status open - -\begin_layout Chapter Dominios de estabilidad \end_layout -\begin_layout Plain Layout +\begin_layout Standard \begin_inset CommandInset include LatexCommand input filename "n5.lyx" @@ -240,10 +240,5 @@ filename "n5.lyx" \end_layout -\end_inset - - -\end_layout - \end_body \end_document @@ -250,12 +250,12 @@ y una solución aproximada \begin_inset Formula $(t_{i},\omega_{i})_{i=0}^{n}$ \end_inset - por un método multipaso de coeficientes -\begin_inset Formula $a_{0},\dots,a_{m-1},b_{0},\dots,b_{m}$ + por un método multipaso con paso +\begin_inset Formula $h>0$ \end_inset - con paso fijo -\begin_inset Formula $h>0$ + y coeficientes +\begin_inset Formula $a_{0},\dots,a_{m-1},b_{0},\dots,b_{m}$ \end_inset , el @@ -630,7 +630,8 @@ Fijado \begin_inset Formula \begin{multline*} \Vert\tilde{\omega}_{i+1}-\omega_{i+1}\Vert=\Vert\tilde{\omega}_{i}-\omega_{i}+hØ(t_{i},\omega_{i},h)-hØ(t_{i},\tilde{\omega}_{i},h)+\varepsilon_{i}\Vert\leq(1+hL)\Vert\tilde{\omega}_{i}-\omega_{i}\Vert+\Vert\varepsilon_{i}\Vert\leq\\ -\leq(1+hL)^{i+1}\left(\Vert\tilde{\omega}_{0}-\omega_{0}\Vert+\sum_{j=1}^{i}\Vert\varepsilon_{j}\Vert\right)+\Vert\varepsilon_{i}\Vert\overset{(1+hL)^{i+1}\geq1}{\leq}(1+hL)^{i+1}\left(\Vert\tilde{\omega}_{0}-\omega_{0}\Vert+\sum_{j=1}^{i+1}\Vert\varepsilon_{j}\Vert\right). +\leq(1+hL)^{i+1}\left(\Vert\tilde{\omega}_{0}-\omega_{0}\Vert+\sum_{j=1}^{i}\Vert\varepsilon_{j}\Vert\right)+\Vert\varepsilon_{i}\Vert\leq\\ +\overset{(1+hL)^{i+1}\geq1}{\leq}(1+hL)^{i+1}\left(\Vert\tilde{\omega}_{0}-\omega_{0}\Vert+\sum_{j=1}^{i+1}\Vert\varepsilon_{j}\Vert\right). \end{multline*} \end_inset @@ -830,11 +831,15 @@ polinomio característico \end_layout \begin_layout Standard -Dados un método multipaso de paso fijo con -\begin_inset Formula $\omega_{i}:=a_{0}\omega_{i-m}+\dots+a_{m-1}\omega_{i-1}+hF(t_{i},h,\omega_{i-m},\dots,\omega_{i})$ +Dados un método multipaso de paso fijo +\begin_inset Formula +\[ +\omega_{i}:=a_{0}\omega_{i-m}+\dots+a_{m-1}\omega_{i-1}+hF(t_{i},h,\omega_{i-m},\dots,\omega_{i}) +\] + \end_inset - y +y \begin_inset Formula $\omega_{i}:=\alpha_{i}$ \end_inset @@ -932,6 +937,18 @@ Método predictor-corrector \end_layout \begin_layout Standard +\begin_inset ERT +status open + +\begin_layout Plain Layout + + +\backslash +begin{sloppypar} +\end_layout + +\end_inset + Dados un método implícito \begin_inset Formula $\omega_{i}:=F(t_{i},h,\omega_{i-1},\dots,\omega_{i-m})$ \end_inset @@ -976,6 +993,23 @@ corrector \end_inset + +\begin_inset ERT +status open + +\begin_layout Plain Layout + + +\backslash +end{sloppypar} +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard Así se combina la simplicidad de un método explícito con el menor error de uno implícito. Se podría repetir el paso corrector para obtener mejores cotas, pero es |