How to integrate this function numerically?

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Hello everyone,
I'm stuck at this equation and I want to integrate it numerically
where
and r = 695510, a = -0.0021, b = 1.34, Wo = 438.1
I need to integrate the first equation numerically to get V as a function of R
Numerical integration from R = 10, where it is assumed V = U, to 215 should give V(R).
I appreciate your help.
Thank you,
  2 Comments
Mohamed Nedal
Mohamed Nedal on 14 Dec 2019
Yes that's right, it's the base of the natural logarithm and it's being raised to the part after it.

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Accepted Answer

Chuguang Pan
Chuguang Pan on 14 Dec 2019
You can use Euler formula. V(n+1)=V(n)+h*f(R,V(n)), which f(R,V) is the right side of differential equation.
But you need to know the initial value V(10).
r=695510;a=-0.0021;b=1.34;Wo=438.1;
h=0.1;%Integral step size, you can change this value
N=100;%It means that you want to integral from 10 to 10+h*N
V=zeros(1,N+1);%Initialization V array
V(1)=?;%Need to know the initial value V(10)
for n=1:N
R=10+(n-1)*h;
W=Wo*sqrt(1-exp(1)*(2.8-R)/8.1);
V(n+1)=V(n)+h*r*a*R^(-b)*(1-W/V(n));
end
X=10+(0:N)*h;
Y=V;
plot(X,Y);
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