Howdy all,

I am trying to create a solar system model by defining a force equation then using the sequence function to create a differential equation and then solving those differential equations using the initial conditions (in X,Y,Z coordinates). So far I have the code below.

Download ass4.mw

Everything works fine until I try to execute the last line. When I do that I get an error that says "Error, in dsolve/numeric/process_input. invalid specifications of initial conditions.

At this point I am not sure if the problem lies in how I have defined my initial conditions or the way i've defined the force equation but I am open to any suggestions or ideas on where I should go from here.

Thanks in advance!

Nick

Howdy all,

I am trying to fit an exponential and logistical model to a set of population data i've been given using the NonlinearFit function in the statistics toolbox. When try to find the fit for the exponential function I get an error saying "SVD of estimated Jacobian could not be computed". Furthermore, when I display the regression over the set of data points all it shows is a horizontal line. I'm not sure how to go about fixing this. My data set is only 17 points and my input function is about as simple as it gets.

When I run the program to solve for logisitcal model I do not get the error but the displayed plot still shows just a horizontal line dispite the function being non-linear.

So far I have...

regE := NonlinearFit(a*exp(b*x),year,population,x)

regLog := NonlinearFit(a/(1+b*exp(-c*x)),year,population,x)

expon := plot((regE), x = 1850..2020):

logi := plot((regLog), x = 1850..2020):

display({data,logi,expon});

I have not tried using optimization yet but I will soon although I'm not sure if it will improve my results since my undertanding is that they both use the same process to estimate the parameters.

Anyways, Thanks for the help in advance!!

EDIT: Here is the data I am using.

year := [1850,1860,1870,1880,1890,1900,1910,1920,1930,1940,1950,1960,1970,1980,1990,2000,2010]:

population :=[4668,9070,17375,27985,37249,63786,115693,186667,359328,528961,806701,1243158,1741912,2049527,2818199,3400578,4092459]:

Howdy,

I am trying to create a mathmatical model that shows a predator-prey relationship along with seasonal variations (hibernation). I made two piecewise functions where one is "on" during the winter and the other is "off" during the winter and the model worked well for one unit of time. 

My problem is that I would like the piecewise functions to apply over an arbitrary amount of time units periods without having to set the range within the function itself for 100 units of time. I was thinking that a for loop would work but i'm not sure how I would impliment that.

Thanks in advance!!

Edit: 

Here's a little bit more info on the problem.

I have three O.D.E's in an array..

ode := {r'(t),h'(t),c'(t)}

which are dependent on a list of parameters..

constants := {a,b,...,s,w,c0,h0,r0};

where s and w are my piecewise functions.

I am able to solve the three odes using dsolve for one period of s and w.

Again, I'm really not sure where to start to make my model periodic.