how to intergrate my acceleration vs time curve to velocity vs time curve with simpson's rule, instead of using cumtrapz?

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CHUNG CHIEH GAN 2020-4-12

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回答： Thiago Henrique Gomes Lobato 2020-4-12

i have a data set of acceleration vs time, i need to intergrate it into velocity vs time and also displacement vs time. anyone can help me with numerical simpson's rule instead of using cumtrapz?

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Answer 1

Thiago Henrique Gomes Lobato 2020-4-12

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You need to implement the simpson's rule on your own. A naive implementation would be something like that

f = @(t)t.^2; 
N = 1000;
ti = 0;
tend = 5;
h=(tend-ti)/N; 
t=linspace(ti,tend,N);
F = 0;
for i = 1:N-1
F  = F + (h/6)*(f(t(i))+(4*f((t(i)+t(i+1))/2))+f(t(i+1)));
end
% To verify the result
AnalyticalResult = tend^3/3;
Error = (AnalyticalResult-F)/AnalyticalResult
Error =
   1.0000e-03