October 17 2006
bjain 8
Download 569_ODE-25 Reactions.doc
Hi,
I want to solve 25 set of differential equation for unknown variable and contants.
Problem Statement: Solve the following set of differential equations for concentrations terms in terms of CA0 and t
CA, CB, CC, CD, CE, CF, CG, CH, CI, CJ, CK, CL, CM, CN, CP are the variables and k1 to k25 and CAO are constants
Initial Values: t=0 CA=CA0 and CB=CC=CD=CE=CF=CG=CH=CI=CJ=CK=CL=CM=CN=CP =0
How do I proceed for the same?
Regards,
Bikash

Hi,
I am trying to use fsolve to find the roots of p non-linear equations. These vary from 2 dimensional to, so far, 5 dimensional.
I'm really trying to minimize the log likelihood of an ARCH time series:
L := (t) -> 1/2*T*log(2*Pi)+1/2*Sum(log(h(t)),t = p .. T)+1/2*Sum(y[t]^2/h(t),t = p .. T):
where
h := (t) -> alpha[1] + alpha[2]*y[t-1]^2 + alpha[3]*y[t-2]^2 ... + alpha[p]*u[y-p]^2:
and
y[t] are observed data.
I've used the p partial derivatives to solve for dL/dalpha=0 using fsolve and intervals alpha=0..1. Occasionally, it works fine and estimates the parameter vector alpha reasonably. However, sometimes it takes about 30-60 seconds and just returns the equation and no answer:

October 10 2006
Rick 28
Hi,
I have a question about Gröbner bases and using the Rosenfeld_Grobner algorithm in diffalg. What is best to use? If the equations only contain time differentiated variables, is it better to differentiate the equations "by hand" first and let the Gröbner package deal with the problem or is it better to just plug the whole thing into diffalg from the start?

Given N-1 independent (not necessarily linear) equations in N variables, how do I tell Maple to find solutions in terms of a specific variable?
For example:
with(RealDomain);
eq1:=x-1=a*cos(theta);
eq2:=x+1=a*sin(theta);
I want to find a and theta in terms of x:
a=sqrt(2*x^2+2), theta=arctan((x+1)/(x-1))
solve({eq1,eq2},[a,theta]) appears to give me solutions based on elimination of x.

Dear All,
I'm working on a problem in differential equations where I need to compute the n-th power of a differential expression. Can Maple be taught to differentiate polynomial functions without carrying out the multiplications / simplifications that it usually does? For example:
diff(-2*c/x^3,x); gives the answer 6*c/x^4.
I want it to return: (-3)(-2)*c/x^4.
Ideally, I also do not want it to simplify sums of such results.
Thank you very much, I appreciate your help!
Andrea Bruder

Hi there!
I have a system of four non-linear equation that I can solve with fsolve after having provided the parameter values. I wrote a procedure which passes the parameters values, define all the equations and call for fsolve which provides the solution value for all the four unknowns.
Now, I would like to plot each solution against the input parameters passed to the procedure. In other words, I want to make some comparative statics which shows as the solution changes as the parameters change. Of course, I'll make only two parameters varying simultaneously.
I tried plot3d, but it doesn't work, because the procedure is not really a function I guess.

The attached file solves a system of equations in a couple of seconds in maple 9.5
But in classic worksheet maple 10.04 after many minutes it gobbles up gigabytes of memory and then ends with an error.
The file belows shows the details but it has the form
sys:={eq1,...eq22}:
solution:=solve(sys,{var1,...var22}):
Any comments very much appreciated.
Download 2129_No Solve.mws

Hi.

I am trying to debug a small piece of code I've written.

I have a procedure for solving some quite complex equations. For single points in space.

I have a procedure that:

has some quantities passed to it,

brings in a 2 by 80

Does a for loop for each of the rows in the data, to take the first col value, and puts that along with the vars passed to it into the first procedure. It then works out the difference between the value given by the first procedure and the second col. Squares this and adds it to the total.

I'd like to use the NPLSolve minimize function to minimise this total squared sum of differences, by passing differnt values to the second function.

September 04 2006
yvette 8
Hi
I'm new to Maple. I've had it for years and am just now getting into it. My problem is how to simultaneously solve a set of equations that feature some nonlinear terms. This isn't a set ODE's. They are algebraic equations with nonlinear integral terms like, I2:=int(cos(Pi/2/Theta*e)^4.545*sin(e)*cos(e-phi),e=theta..Theta); There are 3 variables to solve for after the variable theta has been specified. Equation 1 has the nonlinear terms and the other 2 equations are linear. I can post all 3 equations if someone can help.
I saw an example on this site for a vibration problem solved with the Runge-Kutta method but the dsolve command was used and mine aren't ODE's. I have version 7.

August 31 2006
Mak07 8
I am solving a set of equations with 4 variables. The solve comes out as an unordered set each time and I cannot figure out how to sort them. Btw, I am using Maple V Release 4 (yes it is old. :-))

So here is the results of the solve

sols := {b1 = 84.92147612, b4 = 87.31363038, b2 = 101.6273403, b3 = 86.10094107}

What i need to get is either the solution ordered {b1,b2,b3,b4} or the indices of the variables in order. I have tried the following:

Isort:=proc(L) local a,i;

> a:=sort([$1..nops(L)],evalb((i,j)->L[i]<=L[j])); [seq(L[i],i=a)],a end:

as recommended from another post and i get the following error:

Hi,
I'm very new to Maple. I have a set of equations. 16 equations with 16 unknowns, so it is possible to solve for 16 unknowns. I can solve using matrix if all of these equations are linear using my calculator; however, 2 out of the 16 equations are non-linear (x^2...ect) equations. I would like to use a software to solve for it.
Is there a way to solve these 16 equations using Maple?
If there is, please show me how, the more details the better for me because I'm very new to Maple and not very familiar with using Maple user interface.
Thanks

I have been using solve in Maple 9.5 to solve a system of equations with a very large solution (90,000 terms provided in about 10 mins). Access to Maple 9.5 was unvailable so I used Maple 9; I gave up waiting after several hours and seeing memory use go up to 1Gb. Is there a big difference in the coding to explain this. Also, I don't yet have Maple 10; does it have any further improvements?

As currently programmed, fsolve() does not do numerical derivatives for systems of equations. The reason for this is that subs() is used instead of eval() when evaluating derivatives. [Note: jacob is the symbolically defined jacobian of the system of equations and lsub is the sequence of appropriate numerical substitutions (not the "list" of substitutions the mnemonic might suggest).] The original statement (in `fsolve/sysnewton`) is:
A:=traperror(evalf(subs(lsub,jacob),Digits-5+n));
The functions evalf() and subs() apparently do no know how to work together to produce numerical derivatives. However, the following statement does work.

I have seen a number of forum questions concerning showing students the steps in a problem. There seems to be some confusion about how to do this reliabley and easily.
A method I have found useful is seen below:

I wish to extract the coefficients associated with a particular variable.
I have assigned the results of a symbolic solve of a system of equations (sol) using
assign(sol):
One of the assigned variables in (sol) is ROLL and the symbolic solution is of the form
ROLL;
200*a*b^2*VAR1 + 3000*b*VAR2 + 1500*cos(c)*d*VAR1 . . .
(the actual expression is hundreds of line long and each VAR is randomly distributed in the expression)
How do I isolate the coefficients associated with a specific VAR
eg for VAR1 I want to be able to make the assignment
coefVAR1:=(200*a*b^2)+(1500*cos(c)*d)