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Implement problem 5 and a bit more

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Cory Balaton 2023-09-10 12:41:15 +02:00
parent 1ab0a1a490
commit 46d3a78767
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5 changed files with 11 additions and 9 deletions
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latex/assignment_1.pdf Normal file
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latex/assignment_1.tex
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@ -80,7 +80,7 @@
\begin{document} \begin{document}
\title{Project 1} % self-explanatory \title{Project 1} % self-explanatory
\author{Cory Balaton \& Janita Willumsen} % self-explanatory \author{Cory Alexander Balaton \& Janita Ovidie Sandtrøen Willumsen} % self-explanatory
\date{\today} % self-explanatory \date{\today} % self-explanatory
\noaffiliation % ignore this, but keep it. \noaffiliation % ignore this, but keep it.
@ -107,4 +107,6 @@
\input{problems/problem9} \input{problems/problem9}
\input{problems/problem10}
\end{document} \end{document}

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latex/problems/problem1.tex
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@ -40,5 +40,5 @@ Using the values that we found for $c_1$ and $c_2$, we get
\begin{align*} \begin{align*}
u(x) &= -e^{-10x} + (e^{-10} - 1) x + 1 \\ u(x) &= -e^{-10x} + (e^{-10} - 1) x + 1 \\
&= 1 - (1 - e^{-10}) - e^{-10x} &= 1 - (1 - e^{-10})x - e^{-10x}
\end{align*} \end{align*}

4
latex/problems/problem5.tex
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@ -1,6 +1,6 @@
\section*{Problem 5} \section*{Problem 5}
\subsection*{a)} \subsection*{a \& b)}
\subsection*{b)} $n = m - 2$ since when solving for $\vec{v}$, we are finding the solutions for all the points that are in between the boundaries and not the boundaries themselves. $\vec{v}^*$ on the other hand includes the boundary points.

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latex/problems/problem6.tex
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@ -14,12 +14,12 @@ Following Thomas algorithm for gaussian elimination, we first perform a forward
\begin{algorithm}[H] \begin{algorithm}[H]
\caption{Foreward sweep}\label{algo:foreward} \caption{Foreward sweep}\label{algo:foreward}
\begin{algorithmic} \begin{algorithmic}
\State Create new vector \vec{\hat{b}} of length n. \State Create new vector $\vec{\hat{b}}$ of length n.
\State \hat{b}[0] &= b[0] \Comment{Handle first element in main diagonal outside loop} \State $\hat{b}[0] = b[0]$ \Comment{Handle first element in main diagonal outside loop}
\For{$i = 1, ..., n-1$} \For{$i = 1, ..., n-1$}
\State d = \frac{a[i-1]}{b[i-1]} \State $d = \frac{a[i-1]}{b[i-1]}$
\State b -= d*(*sup_diag)(i-1); \State $b -= d*(*sup_diag)(i-1);$
(*g_vec)(i) -= d*(*g_vec)(i-1); $(*g_vec)(i) -= d*(*g_vec)(i-1);$
\EndFor \EndFor
\While{Some condition} \While{Some condition}
\State Do something more here \State Do something more here