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Numerical integration of an ODE?

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KLETECH MOTORSPORTS
KLETECH MOTORSPORTS 2020-11-14
回答： Priyanka Rai 2020-11-18
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
  2 个评论
John D'Errico
John D'Errico 2020-11-14
Read the help for ODE45. You will find examples in there.
doc ode45
riccardo
riccardo 2020-11-16
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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回答（1 个）

Priyanka Rai
Priyanka Rai 2020-11-18
To be able to integrate 2nd Order ODE numerically you can use the following methods, based on your use case:
  1. If function f is to be integrated, then for definite integral you can use
int(f, a, b)
Refer this link : https://www.mathworks.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(fun,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 : https://www.mathworks.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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