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I'm considering a system of differential equations given by dR/dt = U and dU/dt = (L-GM)/R^2. I'm trying to use RK4 to solve this system and generate some plots. My code is given below, however I'm not generating any plots. Is therefore something wrong with my RK4 code? Note that the code does run.
function [x,t] =nma_RK4_4( )
delT = 0.001; %time grid
t = linspace(0,5,round(5/delT)); %time
N = length(t);
x = zeros(2,N);
x(1,1) = 100000; %initial conditions
x(2,1) = 100000;
G = 6.67*power(10,-11);
M = 1.5*1.989*power(10,41);
L = x(1,1)*x(2,2);
theta = -x(2,1)/(power(x(1,1),2));
xvar = x(1,1)*cos(theta);
yvar = x(1,1)*sin(theta);
for i = 1:(N-1)
k1 = delT * f( t(i) , x(:,i));
k2 = delT * f( t(i)+1/2*delT , x(:,i)+1/2*k1);
k3 = delT * f( t(i)+1/2*delT , x(:,i)+1/2*k2);
k4 = delT * f( t(i)+delT , x(:,i)+k3);
x(:,i+1) = x(:,i)+1/6*(k1+2*k2+2*k3+k4);
end
function r=f(t,x)
r=[x(2)
(L-G*M)/(power(x(1),2))];
end
figure()
plot(xvar,yvar)
end
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Answers (1)
Walter Roberson
on 10 Aug 2016
Your xvar and your yvar are scalars, so plot(xvar,yvar) is plotting only one point. The default when using plot() is to not use any markers, so the one point is not showing up. It would show up if you used plot(xvar, yvar, 'r*-')
Is there a reason you are calculating x but not using it to plot?
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