MaplePrimes Questions

Hi,

I'm trying to solve the following non-linear ODE numerically:

by ececuting

but maple gives me this error-message:

"Error, (in dsolve/numeric/make_proc) Could not convert to an explicit first order system due to 'RootOf'"

I couldnt find any useful information in the manual. What does this error mean? Is there something wrong with my maple code or is there just no solution for this particulare differential equation?

 

Thanks in advance

Hi

I have this PDE and was wondering how I can get Maple to solve it

utt+2ut-uxx=18sin(3πx/l)

with conditions u(0,t)=u(l,t)=0 and u(x,0)=ut(x,0)=0

Thanks

James

 

 

 

Could anyone assist in rectifying this error ''Error, (in fsolve) {f[1], f[2], f[3], f[4], f[5], f[6], f[7], f[8], f[9], f[10], f[11], theta[11]} are in the equation, and are not solved for''. Here is the worksheet FDM_Revisit_1.mw

The "program" below includes a readline statement.  This does not clear the former output when run again.  Is there any modification to correct this?

David

 

restart;
 with(plots):
 with(plottools):
 #f:=proc()
 #local c, numplayers:
 #numplayers:=4:
 #c:= rectangle([0,0], [11,11], color=red):
 #plots[display](c, scaling=constrained, view=[-0.8..11.5,-0.8..12],axes=BOXED);
 printf("Enter the number of players:\n");
 numplayers:=readline(terminal):
 printf("Number of players is %s\n",numplayers);
 #printf("Number of players is %d\n",numplayers);
 #return "foo";
 #end proc:
 #f();

I am using the SumOverRepeatedIndices and get a Length of Output Exceeded error. Sometimes if I close the file and restart the program then I get a result and no error.  However, if I recalculate then I get the error.

 


restart; with(Physics); with(Tetrads)

[e_, eta_, gamma_, l_, lambda_, m_, mb_, n_]

(1)

`#msup(mi("ds",mathcolor = "#af00af"),mn("2",mathcolor = "#af00af"))` := Physics:-`*`(Physics:-`*`(2, dzeta), dzetabar)+Physics:-`*`(Physics:-`*`(2, du), dv)+Physics:-`*`(Physics:-`*`(2, H(zeta, zetabar, u, v)), (du+Physics:-`*`(Ybar(zeta, zetabar, u, v), dzeta)+Physics:-`*`(Y(zeta, zetabar, u, v), dzetabar)-Physics:-`*`(Physics:-`*`(Y(zeta, zetabar, u, v), Ybar(zeta, zetabar, u, v)), dv))^2)

2*dzeta*dzetabar+2*du*dv+2*H(zeta, zetabar, u, v)*(du+Ybar(zeta, zetabar, u, v)*dzeta+Y(zeta, zetabar, u, v)*dzetabar-Y(zeta, zetabar, u, v)*Ybar(zeta, zetabar, u, v)*dv)^2

(2)

X = [zeta, zetabar, u, v]

X = [zeta, zetabar, u, v]

(3)

PDEtools:-declare(`#msup(mi("ds",mathcolor = "#af00af"),mn("2",mathcolor = "#af00af"))`)

Ybar(zeta, zetabar, u, v)*`will now be displayed as`*Ybar

(4)

Setup(coordinates = (X = [zeta, zetabar, u, v]), metric = 2*dzeta*dzetabar+2*du*dv+2*H(zeta, zetabar, u, v)*(du+Ybar(zeta, zetabar, u, v)*dzeta+Y(zeta, zetabar, u, v)*dzetabar-Y(zeta, zetabar, u, v)*Ybar(zeta, zetabar, u, v)*dv)^2)

[coordinatesystems = {X}, metric = {(1, 1) = 2*H(X)*Ybar(X)^2, (1, 2) = 1+2*H(X)*Ybar(X)*Y(X), (1, 3) = 2*H(X)*Ybar(X), (1, 4) = -2*H(X)*Ybar(X)^2*Y(X), (2, 2) = 2*H(X)*Y(X)^2, (2, 3) = 2*H(X)*Y(X), (2, 4) = -2*H(X)*Y(X)^2*Ybar(X), (3, 3) = 2*H(X), (3, 4) = 1-2*H(X)*Ybar(X)*Y(X), (4, 4) = 2*H(X)*Y(X)^2*Ybar(X)^2}]

(5)

g_[]

g_[mu, nu] = (Matrix(4, 4, {(1, 1) = 2*H(X)*Ybar(X)^2, (1, 2) = 1+2*H(X)*Ybar(X)*Y(X), (1, 3) = 2*H(X)*Ybar(X), (1, 4) = -2*H(X)*Ybar(X)^2*Y(X), (2, 1) = 1+2*H(X)*Ybar(X)*Y(X), (2, 2) = 2*H(X)*Y(X)^2, (2, 3) = 2*H(X)*Y(X), (2, 4) = -2*H(X)*Y(X)^2*Ybar(X), (3, 1) = 2*H(X)*Ybar(X), (3, 2) = 2*H(X)*Y(X), (3, 3) = 2*H(X), (3, 4) = 1-2*H(X)*Ybar(X)*Y(X), (4, 1) = -2*H(X)*Ybar(X)^2*Y(X), (4, 2) = -2*H(X)*Y(X)^2*Ybar(X), (4, 3) = 1-2*H(X)*Ybar(X)*Y(X), (4, 4) = 2*H(X)*Y(X)^2*Ybar(X)^2}))

(6)

NULL

``

eqn1 := SumOverRepeatedIndices(Physics:-`*`(d_[mu](Y(Zeta, zetabar, u, v)), e_[1, `~mu`])) = 0

`[Length of output exceeds limit of 1000000]`

(7)

eqn2 := SumOverRepeatedIndices(Physics:-`*`(d_[mu](Y(Zeta, zetabar, u, v)), e_[2, `~mu`])) = 0

`[Length of output exceeds limit of 1000000]`

(8)

eqn3 := SumOverRepeatedIndices(Physics:-`*`(d_[mu](Y(Zeta, zetabar, u, v)), e_[4, `~mu`])) = x

(1/2)*(-(diff(Y(Zeta, zetabar, u, v), zetabar))*(Y(X)*Ybar(X)+1)*2^(1/2)+(diff(Y(Zeta, zetabar, u, v), u))*2^(1/2)*(Y(X)-Ybar(X))-(diff(Y(Zeta, zetabar, u, v), v))*2^(1/2)*(Y(X)-Ybar(X)))/((-(Ybar(X)^2+1)*(Y(X)^2+1)/(Y(X)-Ybar(X))^2)^(1/2)*(Y(X)-Ybar(X))) = x

(9)

eqn1 := `[Length of output exceeds limit of 1000000]` = 0

`[Length of output exceeds limit of 1000000]` = 0

(10)

algsubs(`[Length of output exceeds limit of 1000000]` = 0, `[Length of output exceeds limit of 1000000]`)

0

(11)

``

simplify(`[Length of output exceeds limit of 1000000]`)

``


Download Derive_Eq_4.4.mw

Hello everyone,

I'm using Maple18, I tried to integrate the function including natural logarithm:

 

But we get the answer:

Is there any simple way to directly convert the answer to the kind of form we want? I cannot not finish the conversion:

 

So the toolbox "IntegrationTools" was used, but finally, we couldn't compute the integral:

 

 However, we can get the correct answer by manually inputting the formula.

 

Using IntegrationTools is pretty nasty and not very convenient, such as the problem I mentioned.

Does anyone have another solution?

In brief the problem can be stated as follows:

 

Given dependent variables Qi i=1,...,N and independent variables xi, yi, and zi i=1,...,N

which are related via the following system of N linear equations with parameters P1, P2 and P3 :

Qi = P1xi+P2yi+P3zi   i=1,...,N

How to find the optimal values of  P1, P2 and P3 which satisfy the above system of linear equations subject to the following constraints:

Pi>=0   i=1,2,3

and  P1>=P2P3

 Without the requirement of P1>=P2P3, the problem can be solved with the Non-negative Least Squares Method of Lawson and Hanson.  But with this additional constraint, I am stuck.  

 

Your suggestions are welcome.

 

 

 

 

I would like to implement a rule for typeseting delayDotProduct in latex exports (in which this expressions appears in plain form). It corresponds to dot products of vectors/matrices with the "." operator. I tried to define 

`latex/Typesetting:-delayDotProduct`:=proc(f1,f2,f3)
sprintf("{ {%s}{%s} }",cat(`latex/print`(f1)),cat(`latex/print`(f2)))
end proc:

which does not do the job. 

Edit:

A related question: How can I make

D[1,1](x)(t)

produce x''(t) in latex output?

Given expr:=sin(n*x); and say I want to find its value at n=1,x=Pi/2, I found I can do

subs({n=1,x=Pi/2},expr); eval(%);

or combine into one

eval(subs({n=1,x=Pi/2},expr); ----(1)

But also one can write

eval(expr,{n=1,x=Pi/2}); ----- (2)

So if someone wants to just find value of expression as above, it seems (2) is much simpler than (1) since no need to call subs, it is done automatically. Is there anything else I am overlooking?

Only problem I see in the above, is that subs() uses different order: subs({},expr), while eval is:  eval(expr,{}); The other way around.

It would have been better if the order was the same in the API, to reduce confusion.

 

 

ds(t)/dt = a*s(t)*(1 - s(t) - m(t)) - b*s(t) 

dm(t)/dt = c*s(t) - d*m(t)

 

need to find steady state of this system ( finding this simultaneously) in maple 

 

How can you do it? 

I am trying to find the root of an equation that involves a procedure and a definite integral (solved numerically). Of course, I don't need the root to be found symbolically, but numerically would be fine. The problem is, I keep getting the error

"Error, (in fsolve) Can't handle expressions with typed procedures"

whenever I try to solve it. Anyone have any ideas? My worksheet is here: Table-1-duplication-mapleprimes.mw 

 

Hi,

I'm trying to fit some parameters to the data of multiple slightly different experiments.

I've written a function which returns the sums of the error for all experiments.

 

The function which has to be minimized does the following:

1) Set parameters for the model ODE based on the input parameters

2) calculate the difference (numeric solution of ODE <-> experimentel data)

3) repeat step 1+2 for all experiments

4) return the sum of all differences

 

The function works as aspected. But when I try to minimize it by calling:

I got an error:

"Error, (in dsolve/numeric/process_parameters) parameter values must evaluate to numeric, got A = A"

For some reason Maple isnt able to set the new parameters of the ODE.

Anyone got an idea how to fix this?

 

Thanks in advance.

 

 

 

I got a problem with solving a second order ODE. 

The ODE is :

-V(xi)+(1/2)*xi*(diff(V(xi), xi))+(1/4)*(diff(V(xi), xi, xi))=-(1/2)*k2*(diff(H(xi), xi))-k1*n*X/E+1+k2

where k1,k2,n,X,E  all are constant.

the condition is :

V(xi) tends to 2*xi^2 as xi tends to infinity.

I used 'dsolve' to solve the equation firstly, and got a solution with two constant C1 and C2, I want to use the condition to elimilate C2, so I used limit(sol,xi=infinity)=2*xi^2. But when I used the command 'limit', I can't get the answer.

Could any one help me? 

Many thanks!!!

Hi,

I'm a newer of maple .I want to prove x=z,y=z from equations of parametric z.But maple don't solve what I want,who can give me a help .thank you

 

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