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This is the code hw2_final.mw

This is the warning 

Warning, The use of global variables in numerical ODE problems is deprecated, and will be removed in a future release. Use the 'parameters' argument instead (see ?dsolve,numeric,parameters )"

 

How to solve it?

Solving an ODE ...

November 23 2015 Inacio 65

Hello,

 I am trying to solve an differential equation in Maple, but I have no response from Maple.Can someone give a look for me? The coefficients a and b cannot be zero.

 Thanks a lot.

 

Download edo_solução_A_U.mw

Hello everybody

I have a system of ODEs that are too large. I am trying to solve this system using Maple. The corrsponding file has been uploaded. I have 2 question. 1- Does anyone know what is the source of error? 2- Is this a high expectation for Maple to solve such a too big system of ODEs. Note: It makes a few minutes to run all the programm.

Thanks in advance

M.mw

Hello

i have an ODE like this:

I sove this ODE with plot order:

with(plots);
odeplot(sol, [x, (3*D1*a+4*D2)*P(x)/((1-q*S(x))*D2)], .5 .. (1/2)*Pi, tickmarks = [[seq((1/10)*i*Pi = (180*i*(1/10))*`°`, i = 1 .. 8)], default]);
my plot work very well. but i need to plot this ODE with five different parameter (q for for instance, q=0.1 & q=0.2 ....) all in one axis. something like this:

plot(sin(x),x=-10..10)hello

I have an ODE plot like this and I want its horizontal axes to be in degree instead of radian, but I don't know how

Hello,

In this procedure I get the error, 

Error, `:=` unexpected

I know what it means I just can't seem to resolve it. Any help would be greatly appreciated! Thank you in advance for looking at this code!

Kind regards,

Gambia Man

HamilMat := proc (K::integer) local ni, mi, nj, mj, N, Hamil, Eigenvec, i, j, res; option remember; global Vij, U, L; N := K^2; ni := Vector(N); mi := Vector(N); nj := Vector[row](N); mj := Vector[row](N); for i to N do for j to K do res := (i+K-j)/K; if type(res, integer) = true then ni[i] := j; nj[i] := j; mi[i] := res; mj[i] := res end if end do end do; Hamil := Matrix(N, shape = symmetric); for i to N do for j from i to N do if i <> j then Hamil(i, j) := Vij(ni[i], mi[i], nj[j], mj[j]) elif i = j then Hamil(i, j) := Vij(ni[i], mi[i], nj[j], mj[j])+(1/2)*(ni[i]^2+mi[i]^2)*Pi^2/L^2 end if end do end do; return Eigenvec := Eigenvectors(Hamil, output = ['values', 'vectors']), Hamil end proc

Error, `:=` unexpected

 

 

Download small_error.mw

 with small step rather than two points?

I had writen my questions into this code hw2_finished.mw And I think there's maybe something wrong with A=[0..130]

I think you can understand what I want by reading this code but if you are confused please let me know.

Hi everyone, I'm a new one to Maple. I've just learnt some basic tools :)

 

This is my task. I tried to record in Maple but I had errors. I don't know why I had problems but I hope you will help me and I will do it.

tkanks

This is the code example_hw2.mw which derives from hw2_I1.mw.

hw2_I1.mw works but example_hw2.mw doesn't work and the differences between two codes are two new function I added to the dsolve which are η(t) and I2(t). The I2(t) is the second part of I1(t) at the interval t>t* which subject to Phi(t*)=0.

So how to make the sentence 'if |(H(t))/(omega)|>1 then eta(t)=0 else eta(t)=arccos(-(H(t))/(omega))' and 'I2(t) = (int(p(t), x = -eta(t) .. eta(t)))/Pi' work?

 

This is the code  hw2_final.mw

 

Let me explain it.

I am sure that the mistakes must be about the expresstion of the I1(t) and I2(t). Actually if you delete I1(t) and I2(t) , the whole code works and get the picture at the bottom. 

What I want is to put the expresstion of the I1(t) and I2(t) into 'sol:=dsolve...' and 'plots...' to get the picture of I1(t) and I2(t) with respect to t. Before the t* which subject to Phi(t*)=0 (The blue line in the picture at the bottom is Phi) I want I1(t) and after t* I want I2(t).

I1(t) = (int(sqrt(2*(H(t)+omega*cos(q(t)))), q(t) = q(t)-2*Pi .. q(t), numeric))/Pi.    what I want of this experesstion is to get  'int(sqrt(2*(H(t)+omega*cos(q(t)))' from  'q(t)-2*Pi' to 'q(t)' by numeric method.This q(t) is the solution of the ODE sys.

For example(the number I used is not true,just for example) , at the point t=20, q(t)=30-2*Pi.

so I1(t)= (int(sqrt(2*(H(t)+omega*cos(x))), x = 30-2*Pi .. 30, numeric))/Pi.The I2(t) I want is similar to I1(t).

 

How can I solve it?

I'm trying to solve the differential equation.

Eq := diff(y(x), x, x) = -(x^2+1)*y(x)+K;

dsolve({Eq, y(-1) = 0, y(1) = 0}, y(x));

But this not work very well.

Best Regards,

I want to solve an ODE from Game Theory, the Cournot competition.

It says

p(q1+r2(q1))+p'(q1+r2(q1))*r2(q1)-c2'(r2(q1))=0

 where, I think,

' means diff(,q1),

c2(q2)=c*q2 for a fixed c in [0,1]

and

p(q)=max(0,1-q).

So c2,p and r2 are functions.r2 goes from [0,inf) to [0,inf).

I look for r2, which should be r2(q1)=(1-q1-c)/2 when correctly solved.

However, the command dsolve says Error in dsolve (divison by 0).

 What is wrong? How do I obtain the solution for r2 in Maple?

 

My goal is to plot the integral J with respect to t and as you can see J is a piecewise function.

This is my code.   hw2_numerical_2.mw

 

Actually it's a problem about adiabatic invariants.

If you want to know the backgroud please see this link.

www.mapleprimes.com/questions/206645-How-To--Numerically--Solve-It-

Hello,

I'm writing a code and I seem to have an issue when trying to implement a procedure. Here is the code:

 

with(plots):

Z := 75; A := 189; k := 14.6; Rm := 8*R; r0 := 10^(-8)*R; c := 137.036; ms := 105.66/(.51100)

fmtoau := 10^(-15)/(0.529177e-1*10^(-9)):

R := 1.1*fmtoau*A^(1.0/(3.0)):

f := proc (x) options operator, arrow; 1/(1+exp(k*(x-1))) end proc:

n0 := 3*Z*k^2/(4*Pi*(Pi^2+k^2)*R^3):

n := proc (r) options operator, arrow; 4*Pi*n0*f(r/R) end proc:

int(r^2*n(r), r = 0 .. Rm);

73.00000007

(1)

plot(n/n0, 0 .. 2*R);

 

v1 := unapply(int(x^2*f(x), x), x):

Vfermi := proc (r) options operator, arrow; -4*Pi*n0*R^2*(R*(v1(r/R)-v10)/r+v2Rm-v2(r/R)) end proc:

Vuniform := proc (r) options operator, arrow; piecewise(r < R, -Z*(3/2-(1/2)*r^2/R^2)/R, -Z/r) end proc:

plot([Vuniform(r), Vfermi(r), -Z/r], r = r0 .. 2*R, V = 1.2*Vfermi(r0) .. 0, legend = ["uniform charge", "Fermi distribution", "point charge"]);

 

``

plotsol1s := proc (E, K, r0, S, col) local Eqns, ICs, fnl, gnl, r, soln; global ms, c; Eqns := diff(fnl(r), r) = gnl(r)*[E+2*ms*c^2-Vuniform(r)]/c-(K+1)*fnl(r)/r, diff(gnl(r), r) = -fnl(r)*[E-Vuniform(r)]/c-(1-K)*fnl(r)/r; ICs := fnl(r0) = 1, gnl(r0) = 0; soln := dsolve({Eqns, ICs}, numeric); plots:-odeplot(soln, [r, fnl(r)], r0 .. S, color = col) end proc:

plotsol1s(-3*10^5, -1, 10^(-10), Rm, red)

Error, (in f) unable to store '[HFloat(0.0)]' when datatype=float[8]

 

``

``


Any help would be greatly appreciated.

 

Gambia Man

 

Hello

I need to solve the Bending Vibration of Euler-Bernouli Beam Problem and I keep getting stuck. I start with a fairly straight forward fourth order differential eq. Using the dsolve command gives me the general solution

Y(x)=A*sin(a*x)+B*cos(a*x)+C*sinh(a*x)+D*cosh(a*x)

Maple insist on using e^(x)+e^(-x) instead on sinh and cosh - but it's the same. So far so good.

My specific problem is a clamped-pinned beam of length l - so my boundary conditions are (correct me if I'm wrong here):

In the clamped end at x=0: Y(0)=0, Y'(0)=0

In the pinned end at x=l: Y(L)=0, Y''(0)=0

Using both the dsolve(ode,ics) and a dsolve(ode) and then solve(ics) both results in the trivial solution Y(x)=0 - which is wrong - I know there is a tan(a*l)-tanh(a*l) solution.

To get a easier and well documented example to solve by hand, I also tried with a simply supported beam. Boundary conditions are then:

Y(0)=Y(l)=0

Y''(0)=Y''(l)=0

Same result - only the trivial solution Y(x)=0 and If you solve it by hand you get a sin(a*l) solution.

 

What am I doing wrong? Is it syntax error on my part or what?

 

I have attached both my maple doc and a pdf with a walkthrough of the correct solution.

Beam_vibration.mw Transverse_vibration_of_beams.pdf

 

Any help would be appreciated

Kind regards

Jacob

 

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