# Difference between revisions of "Numerical Methods for Ordinary Differential Equations"

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\begin{document} | \begin{document} | ||

\section{ Numerical Integration Methods } | \section{ Numerical Integration Methods } | ||

+ | |||

+ | Numerical integration is used to solve ODEs that cannot be solved analytically, generally through discretization of the ODE. Since the conception of the modern computer, numerical integration methods have become an essential tool in the physical sciences and beyond. Here we will describe two of many such methods, along with some sample code. | ||

\subsection*{ The Euler Method } | \subsection*{ The Euler Method } |

## Revision as of 22:36, 10 December 2018

### Short Topical Videos

- Euler Method for ODEs (LearnChemE)
- Runge-Kutta Method Introduction (LearnChemE)
- Monte Carlo Random Sampling (iman)

### Reference Materials

- Euler Method (Wikipedia)
- Runge-Kutta Methods (Wikipedia)
- Monte Carlo Method (Wikipedia)
- Markov Chain Monte Carlo (Wikipedia)

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\def\eval#1{\big|_{#1}}
\def\tr{\nabla}
\def\dce{\vec\tr\times\vec E}
\def\dcb{\vec\tr\times\vec B}
\def\wz{\omega_0}
\def\ef{\vec E}
\def\ato{{A_{21}}}
\def\bto{{B_{21}}}
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\def\bfieldTemplate:\vec B
\def\apTemplate:A^\prime
\def\xp{{x^{\prime}}}
\def\yp{{y^{\prime}}}
\def\zp{{z^{\prime}}}
\def\tp{{t^{\prime}}}
\def\upxTemplate:U x^\prime
\def\upyTemplate:U y^\prime
\def\e#1{\cdot10^{#1}}
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\begin{document} \section{ Numerical Integration Methods }

Numerical integration is used to solve ODEs that cannot be solved analytically, generally through discretization of the ODE. Since the conception of the modern computer, numerical integration methods have become an essential tool in the physical sciences and beyond. Here we will describe two of many such methods, along with some sample code.

\subsection*{ The Euler Method }

\subsection*{ The Runge-Kutta Method }

\section{ Monte Carlo Methods }

\subsection*{ Monte Carlo Sampling }

\subsection*{ Markov Chain Monte Carlo }

\end{document} <\latex>