I have just begun to study Green's functions and made some initial progress on a problem, but now need Maple to make further progress.  Apologies, I have written up the equations in LaTeX form rather than Maple, as my Maple has gotten very rusty.

$\frac{d^4y}{dx^4}=f(x)

y(0)=y'(0)=0, y(1)=y'(1)=0$

I showed that the Green function $G(x,u)$ for this equation satisfies a condition

$\lim_{\epsilon\to0}\bigg[\frac{\partial^3G}{\partial x^3}\bigg]_{x=u-\epsilon}^{u+\epsilon}=1$

and showed that there is continuity of the Green's function and its first and second partial derivatives with respect to $x$ at $x=u$.  The next step is to show that this function has a piecewise definition such that

\[G=\frac{1}{6}x^2(1-u)^2(3u - 2ux -x\] for x between the range 0 and u and such that

\[G(x,u)=\frac{1}{6}u^2(1-x^2)(3x - 2xu - u) for x between u and 1

I am not entirely sure how to do this with pen and paper, so I have reason to believe that it could be a done a lot more easily with Maple, if someone could give some pointers that would be much appreciated.

Hi, i want to plot a function say R(t,n),

plot(R(t), t = 500 .. 50000) how can specify the t can only take intger value in the range of [500, 50000]?

I am looking for something like :plot(R(t), t = 500 .. 50000, assume=integer)

Hi all, I am having the follwing DE:

restart: 
(diff(z(x), x, x))-z(x) - cos(2*x)/(1+delta*z(x)) = 0:

With initial conditions: z(-pi/4)=z(pi/4)=0 and |delta|<<1

I showed by hand by using perturbation theory the second order approximation. The hint was: you can use Maple to check your answer. 

Is there somebody who can help me with this?

I have been attempting to resolve a particular problem to which I have posted a number of questions in the past.  In my attempts I have stumbled onto a number of command syntax issues & inconsistent result outputs.  Each time I try to post questions that appear to me to be separate questions even though it pertains to the same problem.  On numerous occasions a website moderator has deleted my questions unilaterally because the moderator has the opinion the question is identical to a previous question.

Deleting my questions instead of placing them into a previous thread without a response impedes my progress.  I am going to repost this inconsistent output, ONCE again!  If it is directly related to another thread then notify me of the response somehow instead of simply deleting the question.

The following inconsistency as far as I can tell is not explained in any of my previous questions.  I have a series that represents a particular waveform.  The series representation gives a definitive output.  However, when attempting generate the series of the derivative of this waveform (Q3 & Q4), which does exist (Q1 & Q2), MAPLE chokes on that representation & simply continues to evaluate for days & weeks without generating an output.  Why is this?  If anyone gets a definitive result please post it so that I might be able to reproduce the results.

Thanks in advance.

inconsistent_results.mw

Hi, 

I'm currently studying the Rossler Attractor, which is the following system:

.

I have found the points of equilibrium of the system.

But now I need to draw bifurcation diagrams: one for varying a, one for varying b, and one for varying c.

Can someone please help me with a procedure of how to do this?

Thanks in advance.

I have a relatively complicated ODE that i am plotting. One of the variables in particular (B[2211], purple line in the graph) should under go an exponential-like decay to zero, but instead flies off into negative territory  (see graph below) despite having a very simple equation:

problem variable rate of change= -problem variable*constant +linear combination of variables that  are always posotive.

My intuition is that this is because i have somehow used the odeplot tool wrong - possibly due to a problem with stepsizes.

Here is a MWE i've made:

aa_problem_MWE.mw

Let say I want to generate polynomail with unknown coefficients of variable (x,y,z,t,s) of 3-th order (NOT RANDOM ONE!).

Hey!

The more "nodes, compartments, ..." I define the longer my formula (see below) gets. The formula posted below is written for a starting situation of 9 nodes (i,j,k,l,m,p,q,r,s). The problem that I have is that, besides running out of letters to chose from, the formula is getting to long and is not clear anymore (losing the overview). So I'm looking for a way to write it shorter, especially for the bold parts I assume there must be a better way.

B is a 9x9 matrix, n[0]:=1, N:=9

for i in n[0] do for j to N do for k to N do for l to N do for m to N do for o to N do for q to N do for r to N do for s to N do

if B(i, j) = 1 and B(j, k) = 1 and B(k, l) = 1 and B(l, m) = 1 and B(m, o) = 1 and B(o, q) = 1 and B(q, r) = 1 and B(r, s) = 1 and i <> j and i <> k and i <> l and i <> m and i <> o and i <> q and i <> r and i <> s and j <> k and j <> l and j <> m and j <> o and j <> q and j <> r and j <> s and k <> l and k <> m and k <> o and k <> q and k <> r and k <> s and l <> m and l <> o and l <> q and l <> r and l <> s and m <> o and m <> q and m <> r and m <> s and o <> q and o <> r and o <> s and q <> r and q <> s and r <> s

then P[loss, i, j, k, l, m, o, q, r, s] := P[loss, i, j, k, l, m, o, q, r]*P[fw, r, s]*P[suppr, i, j, k, l, m, o, q, r]*P[fo, s] else P[loss, i, j, k, l, m, o, q, r] := 0 end if; if P[loss, i, j, k, l, m, o, q, r] <> 0 then print(subs(I = i, J = j, K = k, L = l, M = m, O = o, Q = q, R = r, 'P[loss, I, J, K, L, M, O, Q, R]') = P[loss, i, j, k, l, m, o, q, r]) end if end do end do end do end do end do end do end do end do end do

I tried i<>j<>k<>l<>m<>o<>p<>q<>r<>s but that does't work

P.S.: Do you always have to specify something after ELSE using the IF loop? Actually I just don't want maple to do anything if the conditions are not met but since I then cannot print only the solutions I want (the ones for which the conditions are met) I always end up specifying something after else.

Thanks!!

Does any one know of a trick to make Maple solve this PDE using pdsolve?

restart;
pde:=diff(u(x,t),t)+diff(u(x,t),x)=0;
bc:=u(0,t)=0;
ic:=u(x,0)=x;
sol:=pdsolve({pde,ic,bc},u(x,t));

I have tried all HINTS and assumptions and Maple just returns () as solution.

Mathematica solve this as follows

ClearAll[u,x,t];
pde=D[u[x,t],t]+D[u[x,t],x]==0;
bc=u[0,t]==0;
ic=u[x,0]==x;
sol=DSolve[{pde,ic,bc},u[x,t],{x,t}]

Heavidside theta is basically a unit step function.

Download nn.mw
 

Download nn.mwnn.mw

Maple 2018.

I am surprised Maple pdsolve can't solve this basic heat PDE. it is heat PDE on bar, with left end boundary condition being time dependent is only difference from basic heat PDE's on a bar.

May be a Maple expert can find a work around? I tried all the HINTS I know about.

restart;
#infolevel[pdsolve] := 3:
pde:=diff(u(x,t),t)=diff(u(x,t),x$2);
bc:=u(0,t)=t,u(Pi,t)=0:
ic:=u(x,0)=0:
sol:=pdsolve([pde,bc,ic],u(x,t)) assuming t>0 and x>0;

I also hope this question of mine do not get deleted as well, like the question I posted last night asking why pdsolve ignores assumptions that showed number of examples, was deleted few hrs after I posted it. 

If this question gets deleted, I will get the message that posts showing any problem in Maple software are not welcome here by Maplesoft and I will stop coming here.

Good day sirs,

         I am trying to solve this system of equations attached below, but got the following error message "The use of global variables in numerical ODE problems is deprecated, and will be removed in a future release".

       Anyone with useful informations please.

       Below is attached

how I can remove ROOTOF  from solution?

thanks.

root_of.mw

Hi, I've been doing a few small explore plots where the ranges for the parameters are something like [-1,1], but 0 is a special value which will often need to be set.  The slider, gauge components, ... are a bit fiddly to set with exactly zero using a mouse to drag the value.  Thought about a few different ways to do this

* Right click and set value from the component properties option - a bit fiddly for the user and the graph doesn't immediately update when OK'ed.

* Extra control with a tick to set a zero value (fiddly programming and possible confusing interpretation)

* Slider component and snaptoticks=true

Last option seems to be the easiest all round, but I was wondering why it is only the slider component that has a snaptoticks property - none of the other components seem to support it and a gauge would probably be a more natural component to use.

Thanks in advance

Dear sir I want to plot the graph where the lines are coincides maximize the graph in the same graph.  A sample graph i am attaching .some sample codes are here.

h:=z->1-(gamma2/2)*(1 + cos(2*(Pi/omicron1)*(z - d1 - omicron1))):
K1:=((4/h(z)^4)-(sin(Zeta1)/omega)-h(z)^2+Nb*h(z)^4):
kappa:=Int(K1,z=0..1): 
omicron1:=0.2: omega:=10:d1:=0.2:Zeta1:=Pi/6:

plot( [seq(eval(kappa, Nb=j), j in [0.01,0.02,0.03])], gamma2=0.02..0.1);