I have a program that runs ode15s a few thousand times in order to find a particular solution. However, I'm getting many integration tolerance errors such as the following:
"Warning: Failure at t=5.144337e+02. Unable to meet integration tolerances without reducing the step size below the smallest value allowed (1.818989e-12) at time t."
Such warnings cause the program to slow down drastically, and sometimes even grind to a complete halt. The following is some test code that re-produces the error:
G = 6.672e-11;
M = 6.39e23;
g = 9.81;
T1 = 845000/3;
Isp = 282;
mdot1 = T1/(g*Isp);
xinit_on2 = [72368.8347685214;
3384891.40103322;
-598.36623436025;
-1440.49702235844;
16330.430678033]
tspan_on2 = [436.600093957202, 520.311296453027];
[t3,x3] = ode15s(@(t,x) engine_on_2(t, x, G, g, M, Isp, T1), tspan_on2, xinit_on2)
where the function engine_on_2 contains the system of ODEs that model the descent of a rocket, and is given by,
function xdot = engine_on_2(t, x, G, g, M, Isp, T1)
gamma = atan2(x(4),x(3));
xdot = [x(3);
x(4);
-(G*M*x(1))/((x(1)^2+x(2)^2)^(3/2))-(T1/x(5))*cos(gamma);
-(G*M*x(2))/((x(1)^2+x(2)^2)^(3/2))-(T1/x(5))*sin(gamma);
-T1/(g*Isp)];
end
Having done some testing, it seems that I am getting the integration tolerance warnings because of the use of the atan2 function in
which is used to calculate the flight-path angle of the rocket. If I change atan2 to another function (for example cos or sin) I don't get any integration tolerance warnings anymore (although, due to such a change, my solutions are obviously incorrect). As such, I was wondering if I am using atan2 incorrectly, or if there is a way to implement it differently so that I do not get the integration tolerance errors anymore. Furthermore, could it be that I am incorrect and that it is something other than atan2 that is causing the errors?
