# Problem with numerical integration

1. Apr 7, 2006

### MJCfromCT

Hi all,

I am having trouble numerically integrating a function using Maple 10. Here is a bit of background on the problem:

This problem is asking for two plots, one of the velocity of a sounding rocket with respect to time, and the other being the height of the sounding rocket with respect to time. Gravity and drag act on this rocket.

I have the following equations:

density as a function of altitude
drag coefficient as a function of mach number
mach number as a function of velocity
drag as a function of drag coefficient
thrust as a function of mass flowrate and exhaust velocity
mass as a function of time

This problem asks to create these plots for various values of mass flowrate that I am supposed to set myself (2 kg/s, 2.1 kg/s, 2.2...etc).

The known constants that I have are the following:

specific impulse
exhaust velocity
initial mass
initial velocity
initial height
initial density

After inputting everything into maple, I come up with this differential equation:

sys1 := [diff(v(t),t) = (thrust-drag-mass*9.81)/mass, diff(y(t),t) = v(t)];

I am not great with maple, so I am not sure if this is even the correct syntax.

In my attempt to solve the differential equation, I tried this command:

sol1 := dsolve(sys1, numeric, v(0)=0, y(0)=0);

Unfortunately, this gives me the following error:

Error, (in dsolve/numeric/type_check) insufficient initial/boundary value information for procedure defined problem

Any suggestions as to what may be causing the problem here? If necessary, I can post my entire maple file if more detail is needed. Thanks in advance.

2. Apr 7, 2006

### Tom Mattson

Staff Emeritus
That would be good. In fact, why don't you just attach the maple file. That way those of us who have Maple 10 can just download it and run it.

3. Apr 7, 2006

### MJCfromCT

Hi Tom,

Attached is my Maple 10 file. Thanks in advance.

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4. Apr 8, 2006

### Tom Mattson

Staff Emeritus
OK, I just tried to look at it but unfortunately I have Maple 9.5 at work, and it has a ton of typesetting error messages. I have Maple 10 at home and will look at it when I get there.

5. Apr 10, 2006

### MJCfromCT

I have made some progress with this, but I have switched from Maple to Matlab. Attached are my matlab files. When run, I get an error stating:

"Warning: Failure at t=4.258022e+001. Unable to meet integration tolerances without reducing the step size below the smallest value allowed (1.136868e-013) at time t."

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