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matmxhu

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thanks a lot...

matmxhu 85
November 07 2024
0 0

@C_R  thanks a lot,It seems that there is a certain discrepancy between the software packages and the system, which does not appear to be very harmonious

thanks，how to avoid it...

matmxhu 85
July 24 2021
0 0

@dharr thanks,yes,i know the exact answer, but how to  avoid the problem caused by interval if  no warning message was given.

@vv thanks a lot...

matmxhu 85
May 22 2020
0 0

@vv thanks a lot

thanks，just it...

matmxhu 85
September 14 2017
0 0

@Preben Alsholm thanks a lot

i mean how i can distinguish between a__...

matmxhu 85
September 14 2017
0 0

@ThU for indexed subscripts,i can use indets(poly,'specindex(anything,a)') to acquire a[b], and use "select(has, poly,a[b])" to reach the results,but now,i meet  literal subscripts rather than indexed subscripts,how do i?

thanks...

matmxhu 85
November 19 2015
0 0

@Thomas Richard 

thanks,but i'm afraid you wrote wrong...

matmxhu 85
November 18 2015
0 0

@EugeneKalentev 

 

 

thanks a lot ,i find you wrote p[2] rather than p2.

NULL

NULL

``

> 

with(PDEtools):
> 

PDE := (diff(f(x[1], x[2], p[1], p[2]), x[1]))*p[1]/m-(diff(f(x[1], x[2], p[1], p[2]), p[1]))*(2*k*x[1]-k*x[2])+(diff(f(x[1], x[2], p[1], p[2]), x[2]))*p__2/m-(diff(f(x[1], x[2], p[1], p[2]), p[2]))*(-k*x[1]+2*k*x[2]);

(diff(f(x[1], x[2], p[1], p[2]), x[1]))*p[1]/m-(diff(f(x[1], x[2], p[1], p[2]), p[1]))*(2*k*x[1]-k*x[2])+(diff(f(x[1], x[2], p[1], p[2]), x[2]))*p__2/m-(diff(f(x[1], x[2], p[1], p[2]), p[2]))*(-k*x[1]+2*k*x[2])

 (1)
> 

pdsolve(PDE)

`Warning: Incomplete separation.`

  

______________________________________________________

  

` `

  

PDESolStruc(f(x[1], x[2], p[1], p[2]) = _F4(p[2])+_F5(x[1], x[2], p[1]), [{-2*(diff(_F5(x[1], x[2], p[1]), p[1]))*k*m*x[1]+(diff(_F5(x[1], x[2], p[1]), p[1]))*k*m*x[2]+k*_c[4]*x[1]*m-2*k*_c[4]*x[2]*m+(diff(_F5(x[1], x[2], p[1]), x[1]))*p[1]+(diff(_F5(x[1], x[2], p[1]), x[2]))*p__2 = 0, diff(_F4(p[2]), p[2]) = _c[4]}])

 (2)
> 

NULL
> 

PDE1 := (diff(f(x[1], x[2], p[1], p[2]), x[1]))*p[1]/m-(diff(f(x[1], x[2], p[1], p[2]), p[1]))*(2*k*x[1]-k*x[2])+(diff(f(x[1], x[2], p[1], p[2]), x[2]))*p[2]/m-(diff(f(x[1], x[2], p[1], p[2]), p[2]))*(-k*x[1]+2*k*x[2])

(diff(f(x[1], x[2], p[1], p[2]), x[1]))*p[1]/m-(diff(f(x[1], x[2], p[1], p[2]), p[1]))*(2*k*x[1]-k*x[2])+(diff(f(x[1], x[2], p[1], p[2]), x[2]))*p[2]/m-(diff(f(x[1], x[2], p[1], p[2]), p[2]))*(-k*x[1]+2*k*x[2])

 (3)
> 

pdsolve(PDE1)
> 

PDE2 := (diff(f(x[1], x[2], p[1], p[2]), x[1]))*p[1]/m-(diff(f(x[1], x[2], p[1], p[2]), p[1]))*(2*k*x[1]-k*x[2])+(diff(f(x[1], x[2], p[1], p[2]), x[2]))*p__2/m-(diff(f(x[1], x[2], p[1], p[2]), p[2]))*(-k*x[1]+2*k*x[2]);

(diff(f(x[1], x[2], p[1], p[2]), x[1]))*p[1]/m-(diff(f(x[1], x[2], p[1], p[2]), p[1]))*(2*k*x[1]-k*x[2])+(diff(f(x[1], x[2], p[1], p[2]), x[2]))*p__2/m-(diff(f(x[1], x[2], p[1], p[2]), p[2]))*(-k*x[1]+2*k*x[2])

 (4)
> 

pdsolve(PDE2)

`Warning: Incomplete separation.`

  

______________________________________________________

  

` `

  

PDESolStruc(f(x[1], x[2], p[1], p[2]) = _F4(p[2])+_F5(x[1], x[2], p[1]), [{-2*(diff(_F5(x[1], x[2], p[1]), p[1]))*k*m*x[1]+(diff(_F5(x[1], x[2], p[1]), p[1]))*k*m*x[2]+k*_c[4]*x[1]*m-2*k*_c[4]*x[2]*m+(diff(_F5(x[1], x[2], p[1]), x[1]))*p[1]+(diff(_F5(x[1], x[2], p[1]), x[2]))*p__2 = 0, diff(_F4(p[2]), p[2]) = _c[4]}])

 (5)

``

``

From PDE2,we can see p2 different from p[2],i guess the result should be symmetry rather than Eq.(5)

``

``

``

> 

``
> 

``


Download 7.mw

how i know SolveEquations can solve...

matmxhu 85
July 10 2015
0 0

@Markiyan Hirnyk 

hi，please see my attachment，i slove the equations using DirectSearch v.2,for some parameters ,it can work well,but when i choose some ones,it has been running so a great deal of time(one day and one night) that i'm not even sure solves exists.but once in a while,solves can be found,why? thanks  a lot.

``

> 

restart; with(DirectSearch); Digits := 20

20

 (1)
> 

f := omega__a*alpha^2+omega__b*beta^2+Omega__a*eta^2+Omega__b*chi^2-2*kappa*alpha*beta-(1/2)*Omega__a-(1/2)*Omega__b-4*lambda__b*sqrt(-chi^2+1)*chi*beta-4*lambda__a*sqrt(-eta^2+1)*eta*alpha:
> 

eq := sort([seq(diff(f, i), `in`(i, [alpha, beta, eta, chi]))], length)

[2*omega__a*alpha-2*kappa*beta-4*lambda__a*(-eta^2+1)^(1/2)*eta, 2*omega__b*beta-2*kappa*alpha-4*lambda__b*(-chi^2+1)^(1/2)*chi, 2*Omega__b*chi+4*lambda__b*chi^2*beta/(-chi^2+1)^(1/2)-4*lambda__b*(-chi^2+1)^(1/2)*beta, 2*Omega__a*eta+4*lambda__a*eta^2*alpha/(-eta^2+1)^(1/2)-4*lambda__a*(-eta^2+1)^(1/2)*alpha]

 (2)
> 

``
> 

omega__a := 1;

1

  

1

  

1

  

1

  

.3

 (3)
> 

X := [seq((i-1)*0.3e-1, i = 1 .. 21)]
> 

Y := [seq((i-1)*0.3e-1, i = 1 .. 21)]
> 

X := [.27]:

.27

  

.57

 (4)
> 

sols1 := SolveEquations(map(proc (t) options operator, arrow; convert(t, rational) end proc, eq), AllSolutions, solutions = 15, tolerances = 10^(-10), number = 1500, {alpha = -2 .. 2, beta = -2 .. 2, chi = -1 .. 1, eta = -1 .. 1}, evaluationlimit = 1000000);

Warning,  computation interrupted

  
> 

try g := proc () SolveEquations(map(proc (t) options operator, arrow; convert(t, rational) end proc, eq), AllSolutions, solutions = 7, tolerances = 1/10000000000000, number = 1000, {alpha = -2 .. 2, beta = -2 .. 2, chi = -1 .. 1, eta = -1 .. 1}, evaluationlimit = 1000000) end proc; sols := [timelimit(300, g())] catch: printf("waiting") end try

waiting

  
> 

``

``



Download question_15.07.11.mw

i do it,but another wrong happend "Error...

matmxhu 85
April 20 2015
0 0

@Preben Alsholm 

try           

    g:= proc()           

    solve(eq);           

end proc:          

sols:=[timelimit(300, g())];                  

catch "Error, (in fsolve/polyill) time expired" :
sols:=SolveEquations(eq);

 end try;
in my opinion,"Error, (in fsolve/polyill) time expired",the program still may run,but i meet the program stop after the messege.

why SolveEquations show diffrent solutio...

matmxhu 85
April 19 2015
0 0

@Markiyan Hirnyk

hi, the equations read as 

eq:=[2*x-0.2e-1*y-2.04*sqrt(-v^2+1)*v, 2*y-0.2e-1*x-2.16*sqrt(-u^2+1)*u, 2*u+2.16*u^2*y/sqrt(-u^2+1)-2.16*sqrt(-u^2+1)*y, 2*v+2.04*v^2*x/sqrt(-v^2+1)-2.04*sqrt(-v^2+1)*x] ;

i do as follows using DirectSearch package v.2

i find the solutions not the same,some time the results not much difference,but another,sols1 have one solution,sols2 have three solutions.in some time,some solutions are lost.may i have run the command serveral times? regards.

thanks a lot...

matmxhu 85
July 06 2013
0 0

thanks Edgardo very much，I appreciate your early reply.Provided by Edgardo ,it's right using Maple 17.01.

thanks a lot...

matmxhu 85
July 06 2013

thanks Edgardo very much，I appreciate your early reply.Provided by Edgardo ,it's right using Maple 17.01.

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