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@sursumCorda   ...

delvin 35
February 13 2023
0 0

@sursumCorda 

 

I don't know why it makes an error?...

delvin 35
October 18 2022
0 0

@tomleslie 
 

``

``

> 

restart
> 

with(student)

U := a[0]+sum(-a[i]*tanh(xi)^i, i = 1 .. 1)+sum(-b[i]*tanh(xi)^(-i), i = 1 .. 1)

a[0]-a[1]*tanh(xi)-b[1]/tanh(xi)

 (1)
> 

``
> 

``
> 

``

eq := 6*c^2*U(xi)+9*U(xi)^2*c+3*U(xi)^3-2*(diff(U, `$`(xi, 2)))

6*c^2*(a[0](xi)-a[1](xi)*(tanh(xi))(xi)-b[1](xi)/(tanh(xi))(xi))+9*(a[0](xi)-a[1](xi)*(tanh(xi))(xi)-b[1](xi)/(tanh(xi))(xi))^2*c+3*(a[0](xi)-a[1](xi)*(tanh(xi))(xi)-b[1](xi)/(tanh(xi))(xi))^3-4*a[1]*tanh(xi)*(1-tanh(xi)^2)+4*b[1]*(1-tanh(xi)^2)^2/tanh(xi)^3+4*b[1]*(1-tanh(xi)^2)/tanh(xi)

 (2)
> 

``

simplify(eq); fin1 := simplify(numer(%))

-3*a[1](xi)^3*(tanh(xi))(xi)^6*tanh(xi)^3+9*tanh(xi)^3*a[1](xi)^2*(c+a[0](xi))*(tanh(xi))(xi)^5-6*(c^2+3*c*a[0](xi)+(3/2)*a[0](xi)^2+(3/2)*a[1](xi)*b[1](xi))*tanh(xi)^3*a[1](xi)*(tanh(xi))(xi)^4+(18*tanh(xi)^3*b[1](xi)*(c+a[0](xi))*a[1](xi)+3*tanh(xi)^3*a[0](xi)^3+9*c*tanh(xi)^3*a[0](xi)^2+6*c^2*tanh(xi)^3*a[0](xi)+4*(tanh(xi)-1)*(tanh(xi)+1)*(a[1]*tanh(xi)^4-b[1]))*(tanh(xi))(xi)^3-6*(c^2+3*c*a[0](xi)+(3/2)*a[0](xi)^2+(3/2)*a[1](xi)*b[1](xi))*tanh(xi)^3*b[1](xi)*(tanh(xi))(xi)^2+9*tanh(xi)^3*b[1](xi)^2*(c+a[0](xi))*(tanh(xi))(xi)-3*b[1](xi)^3*tanh(xi)^3

 (3)

subs(tanh(xi) = Psi, fin1); fin := simplify(%)

-3*a[1](xi)^3*Psi(xi)^6*Psi^3+9*Psi^3*a[1](xi)^2*(c+a[0](xi))*Psi(xi)^5-6*(c^2+3*c*a[0](xi)+(3/2)*a[0](xi)^2+(3/2)*a[1](xi)*b[1](xi))*Psi^3*a[1](xi)*Psi(xi)^4+(18*Psi^3*b[1](xi)*(c+a[0](xi))*a[1](xi)+3*Psi^3*a[0](xi)^3+9*c*Psi^3*a[0](xi)^2+6*c^2*Psi^3*a[0](xi)+4*(Psi-1)*(Psi+1)*(Psi^4*a[1]-b[1]))*Psi(xi)^3-6*(c^2+3*c*a[0](xi)+(3/2)*a[0](xi)^2+(3/2)*a[1](xi)*b[1](xi))*Psi^3*b[1](xi)*Psi(xi)^2+9*Psi^3*b[1](xi)^2*(c+a[0](xi))*Psi(xi)-3*b[1](xi)^3*Psi^3

 (4)

for i from 0 to degree(fin, Psi) do EQ[i] := simplify(coeff(fin, Psi, i)) end do

Error, final value in for loop must be numeric or character

  

``

``

``


 

Download ger01.mw

@tomleslie       T...

delvin 35
October 17 2022
0 0

@tomleslie 

  

  Thank you for taking time out of your busy day.
   Sincerely,

   delvin

@rcorless    ok...

delvin 35
October 16 2022
0 0

@rcorless 

   The equation is correct, but I didn't pay attention, I wrote some in my own language,sorry.

@Rouben Rostamian      S...

delvin 35
October 16 2022
0 0

@Rouben Rostamian  

   Sorry, I was not paying attention.

      Thanks ocean.

@tomleslie   Ok, I want to ch...

delvin 35
October 10 2022
0 0

@tomleslie 

 Ok, I want to check the different solutions of the equation.

 

  Thanks a million, You made my day.

 

@tomleslie    Thank osean...

delvin 35
October 09 2022
0 0

@tomleslie 

   Thank osean very much for your time.

 "Because the answers are not what I want , The answers obtained are obvious."

m4.mw

@Joe Riel  This is the code I ...

delvin 35
October 09 2022
0 0

@Joe Riel 

This is the code I wrote, but it didn't get a good answer

> 

restart
> 

with(student)

U := a[0]+sum(-a[i]*tanh(xi[n])^i, i = 1 .. 1)+sum(-b[i]*tanh(xi[n])^(-i), i = 1 .. 1)

a[0]-a[1]*tanh(xi[n])-b[1]/tanh(xi[n])

 (1)
> 

u(xi[n+1]) := a[0]-a[1]*(tanh(xi[n])+tanh(d))/(1+tanh(xi[n])*tanh(d))-b[1]*(1+tanh(xi[n])*tanh(d))/(tanh(xi[n])+tanh(d))

a[0]-a[1]*(tanh(xi[n])+tanh(d))/(1+tanh(xi[n])*tanh(d))-b[1]*(1+tanh(xi[n])*tanh(d))/(tanh(xi[n])+tanh(d))

 (2)
> 

u(xi[n-1]) := a[0]-a[1]*(tanh(xi[n])-tanh(d))/(1+tanh(xi[n])*tanh(d))-b[1]*(1+tanh(xi[n])*tanh(d))/(tanh(xi[n])-tanh(d))

a[0]-a[1]*(tanh(xi[n])-tanh(d))/(1+tanh(xi[n])*tanh(d))-b[1]*(1+tanh(xi[n])*tanh(d))/(tanh(xi[n])-tanh(d))

 (3)

eq := c*(diff(U, xi))-(U^2+U*beta+alpha)*(u(xi[n+1])-u(xi[n-1]))

-((a[0]-a[1]*tanh(xi[n])-b[1]/tanh(xi[n]))^2+(a[0]-a[1]*tanh(xi[n])-b[1]/tanh(xi[n]))*beta+alpha)*(-a[1]*(tanh(xi[n])+tanh(d))/(1+tanh(xi[n])*tanh(d))-b[1]*(1+tanh(xi[n])*tanh(d))/(tanh(xi[n])+tanh(d))+a[1]*(tanh(xi[n])-tanh(d))/(1+tanh(xi[n])*tanh(d))+b[1]*(1+tanh(xi[n])*tanh(d))/(tanh(xi[n])-tanh(d)))

 (4)
> 

U := a[0]-a[1]*tanh(xi[n])-b[1]/tanh(xi[n])

a[0]-a[1]*tanh(xi[n])-b[1]/tanh(xi[n])

 (5)

simplify(eq); fin1 := simplify(numer(%))

-2*(tanh(xi[n])^4*a[1]^2-a[1]*(beta+2*a[0])*tanh(xi[n])^3+(beta*a[0]+a[0]^2+2*a[1]*b[1]+alpha)*tanh(xi[n])^2-b[1]*(beta+2*a[0])*tanh(xi[n])+b[1]^2)*tanh(d)*((b[1]*tanh(d)^2-a[1])*tanh(xi[n])^2+2*tanh(xi[n])*tanh(d)*b[1]+tanh(d)^2*a[1]+b[1])

 (6)

subs(tanh(xi[n]) = Psi, fin1); fin := simplify(%)

2*(Psi^4*a[1]^2-a[1]*(beta+2*a[0])*Psi^3+(beta*a[0]+a[0]^2+2*a[1]*b[1]+alpha)*Psi^2-b[1]*(beta+2*a[0])*Psi+b[1]^2)*((-Psi^2*b[1]-a[1])*tanh(d)^2-2*Psi*tanh(d)*b[1]+Psi^2*a[1]-b[1])*tanh(d)

 (7)

for i from 0 to degree(fin, Psi) do EQ[i] := simplify(coeff(fin, Psi, i)) end do

2*a[1]^2*(-b[1]*tanh(d)^2+a[1])*tanh(d)

 (8)

Eqs := {seq(EQ[i], i = 0 .. 6)}

Sol := solve(Eqs, {c, a[1], b[1]})

{c = c, a[1] = 0, b[1] = 0}

 (9)

 

Download m3.mw

@acer  okey...

delvin 35
September 12 2022
0 0

@acer 

okey

@dharr  thanks an ocean...

delvin 35
July 30 2022
0 0

@dharr thanks an ocean

How can I compare the values of A_0, A_1...

delvin 35
July 30 2022
0 0

@dharr Thanks

NULL

> 

restart;
with(PDEtools):
> 


pde2:=-lambda*diff(y(xi),xi)+y(xi)*diff(y(xi),xi)+diff(y(xi),xi$2)=0;

-lambda*(diff(y(xi), xi))+y(xi)*(diff(y(xi), xi))+diff(diff(y(xi), xi), xi) = 0

 (1)
> 

 

NULL

> 

phi(xi):=(p[1]*exp(q[1]*xi)+p[2]*exp(q[2]*xi))/(p[3]*exp(q[3]*xi)+p[4]*exp(q[4]*xi));
eval(phi(xi),[p[1]=I,p[2]=-I,p[3]=1,p[4]=1,q[1]=I,q[2]=-I,q[3]=I,q[4]=-I]);
simplify(%);
phi(xi):=%;
U(xi):=A[0]+sum(A[d]*phi(xi)^d,d=1)+sum(B[d]*phi(xi)^(-d),d=1);

(p[1]*exp(q[1]*xi)+p[2]*exp(q[2]*xi))/(p[3]*exp(q[3]*xi)+p[4]*exp(q[4]*xi))

  

(I*exp(I*xi)-I*exp(-I*xi))/(exp(I*xi)+exp(-I*xi))

  

-sin(xi)/cos(xi)

  

-sin(xi)/cos(xi)

  

A[0]-A[1]*sin(xi)/cos(xi)-B[1]*cos(xi)/sin(xi)

 (2)
> 

subs(y(xi)=U(xi),pde2);

-lambda*(diff(A[0]-A[1]*sin(xi)/cos(xi)-B[1]*cos(xi)/sin(xi), xi))+(A[0]-A[1]*sin(xi)/cos(xi)-B[1]*cos(xi)/sin(xi))*(diff(A[0]-A[1]*sin(xi)/cos(xi)-B[1]*cos(xi)/sin(xi), xi))+diff(diff(A[0]-A[1]*sin(xi)/cos(xi)-B[1]*cos(xi)/sin(xi), xi), xi) = 0

 (3)
 

 

Download test1.mw

@Rouben Rostamian Thanks an ocean...

delvin 35
July 17 2022
0 0

@Rouben Rostamian

Thanks an ocean

Maple code that runs correctly...

delvin 35
July 17 2022
0 0

@Rouben Rostamian 

 

Dear Rouben Rostamian,

thank you for your explanation. You can see where this last part of the code is wrong. It is for balancing and obtaining the balance number.

@Rouben Rostamian   hi,thank you ...

delvin 35
July 17 2022
0 0

@Rouben Rostamian  

hi,thank you

 

Thank you very much for your help
Where is this code wrong?


>
Error, `>` unexpected
restart;
with(PDEtools):
#local gamma:
get_order:=proc(expr,fun,var)
  local the_list,i;
  the_list := convert( indets(expr, function),list);
  PDETools:-difforder(select( i-> has(i, diff(fun,var)),the_list))
end proc:
DGP:=proc(ff,var) local ee;
  ee:=combine(frontend(expand,[ff]),':-power');
  max(map(proc(u,v)
      if u::`*` then
        op(2,combine(select(type,u,
                            identical(v)^anything),
                     ':-power'));
      else
        if type(u,identical(v)^anything) then
          op(2,u);
        else return FAIL end if;
      end if;
    end proc,
    [`if`(ee::`+`,op(ee),ee)],var));
end proc:
  	

fracdiff(u(x,t), x, alpha) assuming alpha > 0, alpha < 1:
FPDE := % + u(x,t)*diff(u(x,t),x) + diff(u(x,t),x,x) = 0;

    /   /         (-alpha) /  d            \              \\
    |   |(x - tau)         |----- u(tau, t)|              ||
    |   |                  \ dtau          /              ||
    |int|-----------------------------------, tau = 0 .. x||
    \   \         GAMMA(1 - alpha)                        //

                 / d         \   / d  / d         \\    
       + u(x, t) |--- u(x, t)| + |--- |--- u(x, t)|| = 0
                 \ dx        /   \ dx \ dx        //    
pde1 := D^alpha*u(x,y,t)+u(x,y,t)*diff(u(x,y,t),x)+diff(u(x,y,t),x$2)=0; 	

tr1 := {u(x,t) = y(xi),  xi = x - v*t^alpha,  v = lambda*t^alpha / GAMMA(alpha+1)};

         alpha                         / d            \
        D      u(x, y, t) + u(x, y, t) |--- u(x, y, t)|
                                       \ dx           /

             / d  / d            \\    
           + |--- |--- u(x, y, t)|| = 0
             \ dx \ dx           //    
   /             alpha                                      \ 
   |     lambda t                     alpha                 | 
  < v = ----------------, xi = x - v t     , u(x, t) = y(xi) >
   |    GAMMA(alpha + 1)                                    | 
   \                                                        / 
 	

pde2:=diff(y(xi), xi, xi) + y(xi)*diff(y(xi),xi) - lambda*diff(y(xi),xi) = 0;

/ d   / d        \\         / d        \          / d        \    
|---- |---- y(xi)|| + y(xi) |---- y(xi)| - lambda |---- y(xi)| = 0
\ dxi \ dxi      //         \ dxi      /          \ dxi      /    
n[1]:=get_order(pde2, U(xi),xi);
el1:=select(has, expand(lhs(pde2)), diff(U(xi), xi$n[1]));
n[2]:=degree(expand(eval(lhs(pde2),diff=0)),U(xi));
el2:=select(has, expand(lhs(pde2)), U(xi)^(n[2]));
eq3:=expand(eval(el1,[U(xi)=a[h]*xi^(-h)]));
eq4:=expand(eval(el2,[U(xi)=a[h]*xi^h]));
d1:=DGP(eq3, xi) assuming h>0;
d2:=DGP(eq4, xi) assuming h>0;
assign(solve(-d1=d2,{h}));
print("N"=h);
                               0
Error, invalid input: diff expects 2 or more arguments, but received 1
                           -infinity
                               0
                              el1
                               0
                              FAIL
                              FAIL
                            "N" = h

 

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