is possible to solve these partial differential equations in maple via pdsolve?

Thanks

In an unrelated thread, I provided the OP with some 1-D code, which contained the Array definition

TC:= Array(0...1001, fill=0)

Note the existence of three '.' characters in the range specification. This was a typo on my part, or my '.' key bounced, or something. The code containing the above definition "worked" with no problem, which, presumably, was why I didn't notice.

The Maple help does state (my emphasis)

Note that more than two dots in succession are also parsed as the range (..) operator.

although I wasn't making use of this fact - I just screwed up when typing the original.

The OP preferred to use 2-D input, and used cut-and-paste to transfer the above code, resulting in 2-D input, which is where the fun started. It seems(?) that when using 2-D input, more than two dots in succession is only interpreted as a straightforward range, if the total number of dots is even.

If the total number of dots is odd, then it appears(?) as if the 'final' dot is associated with the second number in the range as a 'decimal point', (so producing .1001 in the above example). This is then 'coerced/rounded' to an integer - ie it becomes '0', and the above Array definition is interpreted as

TC:= Array(0..0, fill=0)

Consequences in the following code are left to your imagination

Worth an SCR?

K := simplify(C, 'size');
      5                                                  4   
lambda  + (-a__11 - a__33 - a__44 - a__55 - a__22) lambda  + 

  ((a__44 + a__33 + a__22 + a__11) a__55

   + a__44 (a__33 + a__22 + a__11) + (a__33 + a__22) a__11

                                      3                    
   + a__33 a__22 - a__32 a__23) lambda  + (((-a__33 - a__22

   - a__11) a__44 + (-a__33 - a__22) a__11 - a__33 a__22

   + a__32 a__23) a__55

   + ((-a__33 - a__22) a__11 - a__33 a__22 + a__32 a__23) a__44

   + (-a__22 a__33 + a__23 a__32) a__11

                                              2            
   - a__32 (a__13 a__21 + a__24 a__43)) lambda  + ((((a__33

   + a__22) a__11 + a__33 a__22 - a__32 a__23) a__44

   + (a__22 a__33 - a__23 a__32) a__11

   + a__32 (a__13 a__21 + a__24 a__43)) a__55

   + ((a__22 a__33 - a__23 a__32) a__11 + a__13 a__21 a__32) a__44

   + a__32 (a__11 a__43 a__24 - a__21 (a__14 a__43 + a__15 a__53)

  )) lambda + (((-a__22 a__33 + a__23 a__32) a__11

   - a__13 a__21 a__32) a__44

   - a__43 a__32 (a__11 a__24 - a__14 a__21)) a__55

   - a__15 a__21 a__32 (a__43 a__54 - a__44 a__53)

u := [coeffs(K, [lambda], 'l')];
[(((-a__22 a__33 + a__23 a__32) a__11 - a__13 a__21 a__32) a__44

   - a__43 a__32 (a__11 a__24 - a__14 a__21)) a__55

   - a__15 a__21 a__32 (a__43 a__54 - a__44 a__53), 1, 

  -a__11 - a__33 - a__44 - a__55 - a__22, (a__44 + a__33 + a__22

   + a__11) a__55 + a__44 (a__33 + a__22 + a__11)

   + (a__33 + a__22) a__11 + a__33 a__22 - a__32 a__23, ((-a__33

   - a__22 - a__11) a__44 + (-a__33 - a__22) a__11 - a__33 a__22

   + a__32 a__23) a__55

   + ((-a__33 - a__22) a__11 - a__33 a__22 + a__32 a__23) a__44

   + (-a__22 a__33 + a__23 a__32) a__11

   - a__32 (a__13 a__21 + a__24 a__43), (((a__33 + a__22) a__11

   + a__33 a__22 - a__32 a__23) a__44

   + (a__22 a__33 - a__23 a__32) a__11

   + a__32 (a__13 a__21 + a__24 a__43)) a__55

   + ((a__22 a__33 - a__23 a__32) a__11 + a__13 a__21 a__32) a__44

   + a__32 (a__11 a__43 a__24 - a__21 (a__14 a__43 + a__15 a__53)

  )]
u[1] = C__5;
(((-a__22 a__33 + a__23 a__32) a__11 - a__13 a__21 a__32) a__44

   - a__43 a__32 (a__11 a__24 - a__14 a__21)) a__55

   - a__15 a__21 a__32 (a__43 a__54 - a__44 a__53) = C__5
C__1 = u[3];
         C__1 = -a__11 - a__33 - a__44 - a__55 - a__22
C__2 = u[4];
   C__2 = (a__44 + a__33 + a__22 + a__11) a__55

      + a__44 (a__33 + a__22 + a__11) + (a__33 + a__22) a__11

      + a__33 a__22 - a__32 a__23
C__3 = u[5];
C__3 = ((-a__33 - a__22 - a__11) a__44 + (-a__33 - a__22) a__11

   - a__33 a__22 + a__32 a__23) a__55

   + ((-a__33 - a__22) a__11 - a__33 a__22 + a__32 a__23) a__44

   + (-a__22 a__33 + a__23 a__32) a__11

   - a__32 (a__13 a__21 + a__24 a__43)
C__4 = u[6];
C__4 = (((a__33 + a__22) a__11 + a__33 a__22 - a__32 a__23) a__44

   + (a__22 a__33 - a__23 a__32) a__11

   + a__32 (a__13 a__21 + a__24 a__43)) a__55

   + ((a__22 a__33 - a__23 a__32) a__11 + a__13 a__21 a__32) a__44

   + a__32 (a__11 a__43 a__24 - a__21 (a__14 a__43 + a__15 a__53)

  )
 

I am trying to solve a diffusion equation with a potential term that has an integral in it. The equation has the following form: 

PDE := diff(g(x, t), t) = diff((beta(x, t)+diff(g(x, t), x)), x), 

with the function beta: 

beta := proc (x, t) options operator, arrow; int(exp(-abs(x-y))*g(y, t), y = -infinity .. +infinity) end proc

The boundary conditions for the function g(x,t) are simply assumed to be a zero-centered Gaussian in space (i.e. in x). So it is unity for x=0 and zero for the outer boundary that we can set as x=L. 

The problem is easily solved if the function beta is not an integral, but in the current form I get the following error: 
*******
Error, (in pdsolve/numeric/process_PDEs) inconsistent dependencies in PDEs: g(x, t) v.s. g(y, t)

*******

So it does not like the dummy variable in the function g.  

I can not write an additional PDE for beta because my Kernel is an exponential so the integral never goes away. Anyone with a way to solve this?

ADDENDUM: I have now copied the scriptPDE_DIFFUSION_INTEGRAL.mw
 

Download PDE_DIFFUSION_INTEGRAL.mw

below. 

I'm referancing the maple help page: https://www.maplesoft.com/support/help/maple/view.aspx?path=Groebner in my thesis, but I am not sure what fields to include, and what to put in them- particularly for the year.

I am currently facing an issue as regards stability analysis and I will be glad if anyone can offer me some suggestions.  My aim is to have a Theorem in my research stating that the Disease free equilibrium is locally asymptotically stable if R0 (Basic reproduction number) < 1 and unstable if R0 > 1. The same applies to the endemic equilibrium.  I am trying to carry out a stability analysis using Linearization. However, due to the nature of my model, not all my eigenvalues are negative. Below is my Jacobian Matrix:

ROW 1                           ROW 2                       ROW 3                         ROW 4

Column 1:=                                                                                                      

Column 2:=                 -psi                                     0                                   M

Column 3:=                                                                                                           

Column 4:=                 0                                0                                0                        +  M +  -

By using the Routhz Hurwitz criterion, I reduced the matrix block from 4 by 4 to 3 by 3 by using column 4 as co-factor, however, after this matrix reduction, I was still unable to get all terms relating to my basic reproduction number for me to compare and see if the conditions in Routh Criterion is satisfied using the condition R0 < 1 holds.

My Basic Reproduction Number is as follows:

Are there any other methods to  carry out local stability analysis? and Can local stability analysis be done using maple?

Thank you in advance

I can calculate real number eigenvector with QR algorithm from rotation matrix

but this real number is just magnitude of complex number

what is the rotation matrix for calculating complex number?

what algorithm do maple use to calculate fraction eigenvector?

are complex decimal and complex fraction eigenvectors are two different algorithm?

Hello everyone!

how to solve system of 5 equations like as in attachment, but much more faster?

I tried to do this on my computer (CPU 8 Core 3,4 GHz, RAM DDR3 2x8 GB, SSD) but after 12 hour my computer doesn't respond.

What I can do if I don't have a supercomputer?

Forum.mw

Download Rindler_simulation_v2.mw

I want to know about some algorithms used by Maple, if there is a way to dig through the code.

Download 418.mw

Can someone help with the simplification of the result of this code? I am sure the "qs" in the final result should not appear.

Thanking you in anticipation of your positive responses

#k=1
restart:
P:=sum(a[k]*x^k, k=0..2):
assume(alpha>0,alpha <= 1):
Q:=fracdiff(P,x,alpha);
e1:=simplify(eval(P, x=q))=y[n]:
e2:=simplify(eval(Q,x=q))=f[n]:
e3:=simplify(eval(Q,x=q+h^alpha))=f[n+1]:
var:=seq(a[i], i=0..2):
M:=e||(1..3):

Cc:=eval(<var>, solve(eval({M}),{var}) ):
for i from 1 to 3 do
	a[i-1]:=Cc[i]:
end do:
Cf:=P:
E:=collect(Cf, [y[n], f[n], f[n+1]], recursive):
print():
#y[n+1]=collect(simplify(simplify(expand(eval(Cf,x=q+h^alpha)),size)), [y[n],f[n],f[n+1]], factor);
y[n+1]=simplify(eval(Cf, x=q+h^alpha)):
collect(%, [y[n], f[n], f[n+1]], recursive);

Let be given tetrahedron ABCD, where AB = BC = AC = a, AD = d, AD = e, CD = f. I know that, If the measure of angle of AB and CD equal to Pi/3, then we have d^2 - e^2 - a*f = 0. I tried:
ListTools[Categorize];
L := []; 
for a to 30 do for d to 30 do
for e to 30 do for f to 30 do
if abs(d-e) < a and a < d+e and abs(a-e) < d and d < a+e and abs(d-a) < e and e < d+a and abs(d-f) < a and a < d+f and abs(a-f) < d and d < a+f and abs(d-a) < f and f < d+a and abs(e-f) < a and a < e+f and abs(a-f) < e and e < a+f and abs(a-e) < a and a < a+e and -a*f+d^2-e^2 = 0 and igcd(a, d, e, f) = 1 and nops({a, d, e, f}) = 4
then L := [op(L), [a, d, e, f]] end if end do end do end do end do; 
nops(L); 
L;

Another way to find the length of edges of a tetrahedron knowing that the mesure angle of two opposite?

Hello Friends

I have a critical problem that I wish to solve it with maple

suppose we have a list like following: y_obs=(2,4,8,7,9,52,35,478,52) and corresponding variance σy=(.2,.3,.5,.87,.1.2,.22,.78,.99,1.5)
we know y as the function of x described such as y_theoric=x+p and minimizing X is

X=Sigma [(y_theoric-y_obs)^2]/σy which includes the sum of nine numbers...

the question is:

How we can find p from likelihood function and plot general behavior of y versus of x through two above series?

for example this solution used in article under the names Hubble parameter data constraints on dark energy by Yun Chen and Bhatra Ratra (Physics Letters B)

Thank you