Items tagged with equationsequations Tagged Items Feed

Simple Totalizer for dynamic simulation question...

September 12 2007
0 8
Hello again,

I have another simple question. I have a dynamic simulation that I've put together, and I'm solving the system of equations using "dsolve(odeset,numeric)", and all is going well there. However, I added a "product totalizer" that integrates my exit flow with the command:

Ptotal := ptot(t) = int(Fexit, t)

And that works well if the Fexit is a fixed number in my simulation. However, I wanted to change the Fexit variable at certain points in time, so I used the piecewise command:

Fexit := piecewise(and(t >= 25, t < 30), 2, and(t >= 35, t < 34), 2, 0)

The simulation looks fine with the piecewise logic, but the integration above does not. It looks like the integration resets itself to zero where the steps occur. So my questions are:

How do I numerically solve differential equations?...

September 11 2007
0 11
None of the built-in features of Maple will help me numerically solve the kinds of complicated differential equations I want. I was hoping that Maple's option in dsolve of solving by Taylor series would at least grind out the first nine terms of the Taylor series expansion of the solution y(x) of e.g. x^3 + (y'(x) - 9*x)^(5/(y(x)+2)) + 4*(x-y(x))^(y'(6*x+4)) = 0 subject to y(1)=0. I dumped in functional equations, too, to see if Maple could handle it. Ok. So, for something like this, R(x,y(x),y'(x),y'(6x+4))=0 Maple should be at least able to do the first 9 differentiations to express

ODE system difficulties...

September 06 2007
0 2
Hello all, you were very helpful the last time I had a question, I hope you can help me again here. I have a system of differential equations that can be manipulated in two way, each has its own problems 1) I can define the system of equations including a piecewise function. The test of the piecewise involves the ratio st(t)/sz(t) being relative to 1. When I attempt to dsolve,numeric this formalism it gives me an error that it cannot convert to an explicit first-order system (not that I asked it to convert by the way). 2) In place of the piecewise I can have int(1/(1+sqrt(st(t)/sz(t))*sin(theta)),theta=0..Pi) which should evaluate to a real number, and is incidentally where the piecewise function comes from. However then dsolve tells me that it cannot have an integral in a differential equation.

set of eqns, howto auto substitute...

September 06 2007
0 3
Hi all, I'm sort of new to Maple and I got the following problem (just an example): I have 3 equations of the following form: sin(x)=c+d; cos(x)=e+d; tan(x)=e; Now i want to solve the set of eqns to the variable c by automatically substituting d and e. The result should be: c=sin(x)-cos(x)+tan(x) Furthermore it would be very good to know, how to specify which variables should be subsituted and which should remain. I tried variations of eval, subs, algsubs and solve.. Help would be greatly appreciated!

Numeric evolution of a system of ODEs...

August 12 2007
0 8
Hello, I have a problem with a system of ODEs. The three differential equations are as follows: diff(c(t),t) = 2*(c(t))^2 + 21/50*c(t) - 1/100*(h(t))^2 - 1/5*c(t)*h(t) - (9/2000)*h(t) + 49/4000; diff(h(t),t) = h(t)*(c(t) - 1/5*(h(t)-1)); diff(k(t),t) = 8/100*k(t) - h(t) - 1/5*k(t)*h(t); diff(c(t),t) = 2*(c(t))^2 + 21/50*c(t) - 1/100*(h(t))^2 - 1/5*c(t)*h(t) - (9/2000)*h(t) + 49/4000; diff(h(t),t) = h(t)*(c(t) - 1/5*(h(t)-1)); diff(k(t),t) = 8/100*k(t) - h(t) - 1/5*k(t)*h(t); As t goes to infinity the three variables c(t), h(t), k(t), respectively, approach certain values -in this setting 1/50, 11/10, 55/3, respectively- with the values of the derivatives converging to 0. (The point is saddle path-stable.)

Maple 11, Tensors in Physics Package: Possible Bug...

August 10 2007 Maple
0
3
Here are some possible bugs or limitations that I have come across while working with Tensors in the new physics package. I have done best of my efforts looking into the documentation, but it is still possible that the bugs I am listing are not bugs at all but outcome of lack of my knowledge in using Maple. My intention of creating this blog is to not to criticize but to help the Physics package development team in making updates. I appreciate their efforts for developing a much needed package for areas like fluid mechanics, continuum mechanics, theory relativity etc. Platform I am using: Maple Ver 11.01 on Mac OS X 10.4.10

how to find why maple doesn't comlpete the command...

August 06 2007
0 6
We have a maple 10 site license and I recently started to use maple for some challenging symbolic manipulation. Specifically I wanted to find the 3-dimensional eigenvectors A(u,w) and eigenvalues \lambda for a system of 8 partial differential equations. I was disappointed when maple completed most of the problem finding all 8 eigenvalues but only 6 of the 8 eigenvectors. In fact explicitly issuing Eigenvectors(A) command didn't seem to work as it ran for a long time with out returning so I ended up just issuing a series of LinearSolve(A-\lambda I|0) commands. This worked for the first 6 eigenvalues but for the last pair of eigenvalues maple just didn't do anything simply printing the command I issued. Maple didn't print any diagnostic information to let me know what went wrong. My question is when Maple doesn't evaluate a command how does one obtain information about what went wrong?

Elliptic Integrals...

August 05 2007
0 1
I am trying to recreate a transcendental equation from a paper on buckling analysis. I have not been able to successfully manipulate equation (10) given on page 692 of the attached files into the final forms of equations (12) and (13), using the boundary conditions given in (11). Could someone take a look at my Maple worksheet and offer some suggestions that would yield an elliptic integral? Download 4865_Lo_p692.pdf
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Iterating an Equilibrium - fsolve...

August 01 2007
0 5
Hi, I am new to Maple and am having trouble with what should be a simple task. I have a series of simultaneoous equations of the form a*x+b*y=c etc. I have found an initial equilibrium by choosing values of x and y which give me reasonable values of a and b (using the Solve command I have output of a,b,c,x,y which satisfy my equations). Now, I need to use the parameters I have, my a,b,c, to try and retrieve my x and y (my real aim in this is to see the effect on the x,y when I change the a,b,c). When I try and put the equations plus parameter values into Solve it takes a very long time to solve (I stop after 20mins). What I want to do is use the equilibrium values I obtained before to give Maple a starting point to search for a solution.

PDSolve, Error: duplicated elements (ranking)...

July 24 2007
0 3
Hello! I have some trouble with getting an explicit solution to a PDE: f=f(u,v) in IC^4 (IC=complex numbers) So i have a system of 8 equations, first order, integrable (i.e. solution exists by theory). I'm getting the following, when calling pdsolve(PDE, fcns), where PDE is the set of the PDEs and fcns are the 4 complex functions f[i], i=1,2,3,4: "Error, (in pdsolve/sys) duplicated elements (ranking)" What could it be? Thx, yadaddy.

Plotting a function which contains a (difficult) i...

July 13 2007
0 5
Hello, This is related to my recent posts at http://www.mapleprimes.com/forum/integral-equations#comment-8339 I have a function of three variables one of which is inside a (difficult) integral. I want to calculate & store the array of points which satisfy the function, then use transform to change those points and then plot them. The function looks like this: P:=(x,m)->sqrt(x)/(sqrt((x+m)^2-1)*(x+m+sqrt((x+m)^2-1))); IntegralP:=(m)->Int(P(x,m),x=0..infinity); f4A:=(beta,Omega,m)->beta^2+(3*(beta*Omega)^(3/2)*evalf(IntegralP(m)))/(4*2^(3/4))-1; In my earlier case, m=1 (and there was another variable, but it wasn't under the integral) so the integral was not a problem. I tried the same method;

Change coordinate systems for substitutions...

July 13 2007
0 1
Still being a newbie to Maple, I am stuck on this one. I am trying to create a general system of changing my equations in an [x,y] coordinate system to a [u,v] system. As a specific example: I have two substitution equations, u=2x-3y and v=-x+y. I have four equations: x=0, x=-3, y=x, y=x+1. I have tried MapToBasis with both static and procedure statements and I am not having any luck. The equations do not completely change to [u,v]. Here is one example: > proc (u, v) u = 2*x-3*y end proc; > proc (u, v) v = -x+y end proc; > with*VectorCalculus; > SetCoordinates('cartesian', [u, v]);

Plotting functions of several variables...

July 12 2007
0 0
I am trying to plot the equations shown in Figures 5 and 6, which are solutions to Equations (14), (15), and (16). These equations are developed in the Lo paper (attached). I am working through the symbolic solution by hand and would greatly appreciate any suggestions on how to set these equations and the graphs of the same in a worksheet. Thank you for the assistance anyone may offer. Wayne Bell Download 4865_Lo_p691.pdf
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cartesian to polar equations...

July 09 2007
0 2
I am trying to convert equations from cartesian to polar and spherical expecting Maple to change the variables from x,y and z to r, theta, etc. I presume I am using the wrong commands. convert(exp(sqrt(x^2+y^2)),polar) returns the same expression in x and y. What is the correct command? thanks

why won't this plot?...

July 09 2007
0 6
I seem to keep running into things in Maple that I just can't get to plot. I have been using Mathcad and am trying to learn to do everything in Maple, but keep finding myself having to go to Mathcad to do even the simplest things. Could someone please help and explain to me what I'm doing wrong? I have with(plots) and restart() at the top of my page. I then do this: g1 := implicitplot(3x^2,x=0..10,y=0..10); display( g1 ); This results in it just printing the display line again, no graph is shown. I can get this to work using the plot command but since its not very easy in Maple to print multiple equations on a single graph I have started trying to do them this way. If there is a better way to do graphs then please tell me this as well as I'm trying to learn Maple as best as I can.
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