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# Numerical solutions Euler & Runge Kutta

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Need to solve and compare the results of the linear vs non linear pendulum problem. Compare the solutions for the approximation (linear) and numerical(non-linear) using the numerical method runge kutta of 4th DEGREE OR HIGHER(preferrably 4th-6th order). Please include the following details:

1. Detailed explanation of methods used (Euler and runge kutta)
2. Matlab code for both methods and detailed explanation of different variables in code
3. Comparison of methods at different time steps (weaknesses and strengths of both methods)
3. similarities/differences of methods
4. Plots with detailed explanations
5. Videos of pendulum(simulation)-optional if able

https://brainmass.com/math/ordinary-differential-equations/numerical-solutions-euler-runge-kutta-540340

## SOLUTION This solution is FREE courtesy of BrainMass!

Hello, please unzip the attached zip file. The file contains a details pdf file, Euler and Runge Kutta codes. and some plots.

Quick: Linear means maximum displacement angle very small (~5 degree), and approximation is applied as: acceleration considered directly proportional to displacement. Non-linear means angle very large (e.g., 25 degree). Please have a look at all the documents, let me know if you have any difficulty.

There are commands getframe and movie2avi in Matlab, to generate video -- try that.

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