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2018-07-04T16:28:45Z

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nemenman>Ilya at 12:58, 19 February 2018

2018-02-19T12:58:06Z

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{{PHYS212-2018}}

How do we solve systems on nonlinear ODEs in the first place? The Euler method, which we introduced before, is good. But how accurate is it? We will talk about <math>O(dt^n)</math> notation, and we will show that the Euler method is <math>O(dt)</math>. We will verify this by using the scripts that I have uploaded below. We will run the simple Euler method of solving differential equations on the malthusian grows problem with different <math>dt</math>, and show by plotting the error at the end that the error goes down in proportion to <math>dt</math>.

We then will talk about Runge-Kutta methods of solving differential equations. I will add additional notes later on, but for now please use these lecture notes http://web.mit.edu/10.001/Web/Course_Notes/Differential_Equations_Notes/node5.html . Additionally, we discussed how RK2 method is a prediction-correction method.

You will write a different differential equation and will solve it, to show that Runge-Kutta 2 has error <math>O(dt^2)</math>, and the scaling of the error is not a scaling due to the equation being solved, but largely due to the methods used to solve it.

Please [https://docs.google.com/forms/d/e/1FAIpQLSeNvrPddCgvMfHdlSA8uYDddBFqLK81Rrr4l7jfozud6J7iww/viewform submit your work].

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Physics 212, 2018: Lectures 8 - Revision history

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nemenman>Ilya at 12:58, 19 February 2018