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Numerical integration of an ODE?

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KLETECH MOTORSPORTS
KLETECH MOTORSPORTS on 14 Nov 2020
Answered: Priyanka Rai on 18 Nov 2020
Hey! I'm trying to integrate the following 2nd order ODE:
from time t=0 to any random time, say t=50 seconds
ω and A are constants.
I need to integrate the above equation twice, numerically. Any idea how i can do this and what method i'll be using?
thanks
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riccardo
riccardo on 16 Nov 2020
Why numerically ?
If A and w are constants, x(t) = A*sin(w*t) is surely the primitive (plus initial conditions if not zero).

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Answers (1)

Priyanka Rai
Priyanka Rai on 18 Nov 2020
To be able to integrate 2 nd Order ODE numerically you can use the following methods, based on your use case:
  1. If functionfis to be integrated, then for definite integral you can use
int(f, a, b)
Refer this link : //www.tianjin-qmedu.com/help/symbolic/integration.html#:~:text=Integration%20%20%20%20Mathematical%20Operation%20%20,%281%2C%20z%29%29%20or%20int%20%28besselj%20%281%2C%20...%20
2. Numerically evaluate double integral
q = integral2(乐趣、xmin xmax、ymin ymax)
approximates the integral of the function z = fun(x,y) over the planar region xmin ≤ x ≤ xmax and ymin(x) ≤ y ≤ ymax(x) .
Refer this link : //www.tianjin-qmedu.com/help/matlab/ref/integral2.html
Numerical integration functions can approximate the value of an integral whether or not the functional expression is known.When you know how to evaluate the function, you can use integral to calculate integrals with specified bounds.
You can refer to this blog for more information as well: https://blogs.mathworks.com/loren/2014/02/12/double-integra tion-in-matlab-methods-and-handling-discontinuities-singularities-and-more/

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