Dear friends,
I am interested in the solution of the following ODE with maximum accuracy using Euler method.
dy/dt =Ay
where A=[1; 0; 4], is a 3-by-1 matrix. Thank you. How to write a simple MATLAB code using both "for" and "while" loop? Thank you all.
These are just some comments on your question:
1) It will be clearer if you write AT = [1; 0; 4].
2) You have indeed only three independent constant coefficient and linear first order equations with a simple straight solution, one of them is even trivial.
3) There is not much to do to improve the method accuracy, unless you change the method into another one, like Runge-Kutta method.
4) Consider watching this couple of videos. Really all you can do to improve accuracy of the method is to reduce step size (if you really use Euler's method)
https://www.youtube.com/watch?v=b1MOS4cQroU
https://www.youtube.com/watch?v=8cW_CQ77ayI
Programming it should be no problem.
For the equation at hand there's no point in using the Euler method, unless it's to test the code, since the exact solution is immediately found. So just compare the exact solution, with that obtained from Euler's method, for different timesteps and check for which timestep the difference becomes smaller than some bound.
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