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mrbayat

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7 years, 178 days
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Error, (in dsolve/numeric/BVPSolve) unab...

mrbayat 10
January 10 2018
0 0

@Preben Alsholm 

Hi,

I simplified my equations with replacing the ln function by its taylor series. And now I get a new error:

Error, (in dsolve/numeric/BVPSolve) unable to store '-HFloat(0.7260315995144415)-HFloat(4.980143588649368)*I' when datatype=float[8]

GoverningEquations.mw

Error, (in dsolve/numeric/BVPSolve) unab...

mrbayat 10
January 08 2018
0 0

@Preben Alsholm 

Sorry, I changed the initial guess. But I got a new error:

Error, (in dsolve/numeric/BVPSolve) unable to store '-HFloat(0.7260315995138324)-HFloat(4.980143588650197)*I' when datatype=float[8]
GoverningEquations.mw

Error, (in dsolve/numeric/bvp) initial N...

mrbayat 10
January 08 2018
0 0

@Preben Alsholm 

Thanks for your helpful comments. Actually N is function of X2. It was defined wrongly. I corrected it. However I get a new error:

Error, (in dsolve/numeric/bvp) initial Newton iteration is not converging
 

GoverningEquations.mw
 

> 

restart
> 

Ws := (1/2)*N(X2)*k*T*(I1-3-2*log(J));

(1/2)*N(X2)*k*T*(I1-3-2*ln(J))

 (1)
> 

Wm := k*T*((J-1)*log(1-1/J)+chi-chi/J)/nu;

k*T*((J-1)*ln(1-1/J)+chi-chi/J)/nu

 (2)
> 

W := (Ws+Wm-mu*(J-1)/nu)/lambda0^3;

((1/2)*N(X2)*k*T*(I1-3-2*ln(J))+k*T*((J-1)*ln(1-1/J)+chi-chi/J)/nu-mu*(J-1)/nu)/lambda0^3

 (3)
> 

I_1 := lambda1^2+lambda2^2+lambda3^2;

lambda1^2+lambda2^2+lambda3^2

 (4)
> 

J := lambda1*lambda2*lambda3;

lambda1*lambda2*lambda3

 (5)
> 

H := 0.1e-1:
> 

N_in := 0.1e-2:
> 

N_ou := 0.1e-1:
> 

N := proc (X2) options operator, arrow; N_in+(N_ou-N_in)*X2/H end proc;

proc (X2) options operator, arrow; N_in+(N_ou-N_in)*X2/H end proc

 (6)
> 

P := lambda1*(diff(W, lambda1))/J;

(-(0.1e-2+.9000000000*X2)*k*T/lambda1+k*T*(lambda2*lambda3*ln(1-1/(lambda1*lambda2*lambda3))+(lambda1*lambda2*lambda3-1)/(lambda1^2*lambda2*lambda3*(1-1/(lambda1*lambda2*lambda3)))+chi/(lambda1^2*lambda2*lambda3))/nu-mu*lambda2*lambda3/nu)/(lambda2*lambda3*lambda0^3)

 (7)
> 

Pr := simplify(subs(lambda1 = `λr`, lambda2 = `λt`, lambda3 = `λz`, P));

(.1000000000*(-0.1000000000e-1-9.*X2)*k*T/`λr`+k*T*(`λt`*`λz`*ln((`λr`*`λt`*`λz`-1)/(`λr`*`λt`*`λz`))+1/`λr`+chi/(`λr`^2*`λt`*`λz`))/nu-mu*`λt`*`λz`/nu)/(`λt`*`λz`*lambda0^3)

 (8)
> 

Pt := simplify(subs(lambda1 = `λt`, lambda2 = `λr`, lambda3 = `λz`, P));

(.1000000000*(-0.1000000000e-1-9.*X2)*k*T/`λt`+k*T*(`λr`*`λz`*ln((`λr`*`λt`*`λz`-1)/(`λr`*`λt`*`λz`))+1/`λt`+chi/(`λt`^2*`λr`*`λz`))/nu-mu*`λr`*`λz`/nu)/(`λr`*`λz`*lambda0^3)

 (9)
> 

`λr` := lambda0*(diff(r(X2), X2));

lambda0*(diff(r(X2), X2))

 (10)
> 

`λt` := 2*lambda0*theta*r(X2)/L;

2*lambda0*theta*r(X2)/L

 (11)
> 

`λz` := lambda0;

lambda0

 (12)
> 

mu := -0.5e-1:
> 

lambda0 := -1.33*X2+1.482;

-1.33*X2+1.482

 (13)
> 

dsys := [(diff(Pr, X2))/(diff(r(X2), X2))+(Pr-Pt)/r(X2) = 0, subs(X2 = 0, convert(Pr, D)) = 0, subs(X2 = H, convert(Pr, D) = 0)]:
> 

initial := [r(X2) = 2.478367538*X2+0.699e-2, diff(r(X2), X2) = 2.478367538];

[r(X2) = 2.478367538*X2+0.699e-2, diff(r(X2), X2) = 2.478367538]

 (14)
> 

theta := 2.478367538:
> 

T := 295:
> 

L := 0.6e-1:
> 

chi := .1:
> 

k := 1.38064852*10^(-23):
> 

nu := 10^(-28):
> 

indets(dsys, name);

{X2}

 (15)
> 

r_sol := dsolve(dsys, numeric, method = bvp, approxsoln = initial, 'output' = listprocedure)

Error, (in dsolve/numeric/bvp) initial Newton iteration is not converging

  
> 

NULL


 

Download GoverningEquations.mw

 

I will be glad if you could help me.

Thanks

 

Error, (in dsolve/numeric/bvp) initial N...

mrbayat 10
January 08 2018
0 0

Thanks for your comments.

Actually N is function of X2. I it was defined wrongly. I corrected it. This is the worksheet: GoverningEquations.mw.

Unfortunatly I get this error:

Error, (in dsolve/numeric/bvp) initial Newton iteration is not converging
I will be glad if you could help me.

Worksheet file...

mrbayat 10
January 06 2018
0 0

Sorry for corrupted file.

I saved it in two formats (*.mw and *.mws). The files are uploaded both zipped and separately

Maple.zip GoverningEquations.mw GoverningEquations.mws.

Also I paste my worksheet here:

restart;
Ws := (1/2)*N(X2)*k*T*(I1-3-2*log(J));
                 1                             
                 - N(X2) k T (I1 - 3 - 2 ln(J))
                 2                             
Wm := k*T*((J-1)*log(1-1/J)+chi-chi/J)/nu;
                  /          /    1\         chi\
              k T |(J - 1) ln|1 - -| + chi - ---|
                  \          \    J/          J /
              -----------------------------------
                              nu                 
W := (Ws+Wm-mu*(J-1)/nu)/lambda0^3;
              /                              
              |                              
        1     |1                             
     -------- |- N(X2) k T (I1 - 3 - 2 ln(J))
            3 \2                             
     lambda0                                 

              /          /    1\         chi\             \
          k T |(J - 1) ln|1 - -| + chi - ---|             |
              \          \    J/          J /   mu (J - 1)|
        + ----------------------------------- - ----------|
                          nu                        nu    /
I_1 := lambda1^2+lambda2^2+lambda3^2;
                        2          2          2
                 lambda1  + lambda2  + lambda3 
J := lambda1*lambda2*lambda3;
                    lambda1 lambda2 lambda3
H := 0.1e-1;
N_in := 0.1e-2;
N_ou := 0.1e-1;
N := N_in+(N_ou-N_in)*X2/H;
                    0.001 + 0.9000000000 X2
P := lambda1*(diff(W, lambda1))/J;
           1             /  (0.001 + 0.9000000000 X2(X2)) k T   
------------------------ |- --------------------------------- + 
                       3 |               lambda1                
lambda2 lambda3 lambda0  |                                      
                         \                                      

  1  /    /                  /               1           \
  -- |k T |lambda2 lambda3 ln|1 - -----------------------|
  nu |    |                  \    lambda1 lambda2 lambda3/
     |    |                                               
     \    \                                               

                  lambda1 lambda2 lambda3 - 1              
   + ------------------------------------------------------
            2                 /               1           \
     lambda1  lambda2 lambda3 |1 - -----------------------|
                              \    lambda1 lambda2 lambda3/

               chi           \\   mu lambda2 lambda3\
   + ------------------------|| - ------------------|
            2                ||           nu        |
     lambda1  lambda2 lambda3||                     |
                             //                     /
Pr := simplify(subs(lambda1 = `λr`, lambda2 = `λt`, lambda3 = `λz`, P));
                     1                       /  /
-------------------------------------------- |ln|
         2          2          2           3 \  \
λz  λt  λr  nu lambda0      

  λr λt λz - 1\              2          2 
  ---------------------------------| T k λr  λt  
    λr λt λz  /                           

           2
  λz 

   - 0.9000000000 k T λz λt λr nu X2(X2)

                    2          2          2
   - 1. mu λt  λz  λr 

   + (-0.001 nu + 1.) k T λz λt λr + T chi k

  \
  |
  /
Pt := simplify(subs(lambda1 = `λt`, lambda2 = `λr`, lambda3 = `λz`, P));
                     1                       /  /
-------------------------------------------- |ln|
         2          2          2           3 \  \
λz  λt  λr  nu lambda0      

  λr λt λz - 1\              2          2 
  ---------------------------------| T k λr  λt  
    λr λt λz  /                           

           2
  λz 

   - 0.9000000000 k T λz λt λr nu X2(X2)

                    2          2          2
   - 1. mu λt  λz  λr 

   + (-0.001 nu + 1.) k T λz λt λr + T chi k

  \
  |
  /
`λr` := lambda0*(diff(r(X2), X2));
                              / d        \
                      lambda0 |---- r(X2)|
                              \ dX2      /
`λt` := 2*lambda0*theta*r(X2)/L;
                     2 lambda0 theta r(X2)
                     ---------------------
                               L          
`λz` := lambda0;
                            lambda0
mu := -0.5e-1;
lambda0 := -1.33*X2+1.482;
                        -1.33 X2 + 1.482
dsys := [(diff(Pr, X2))/(diff(r(X2), X2))+(Pr-Pt)/r(X2) = 0, subs(X2 = 0, convert(Pr, D)) = 0, subs(X2 = H, convert(Pr, D) = 0)];
initial := [r(X2) = 2.478367538*X2+0.699e-2, diff(r(X2), X2) = 2.478367538];
  [                                   d                      ]
  [r(X2) = 2.478367538 X2 + 0.00699, ---- r(X2) = 2.478367538]
  [                                   dX2                    ]
theta := 2.478367538;
r_sol := dsolve(dsys, numeric, method = bvp, approxsoln = initial, 'output' = listprocedure);
Error, (in dsolve/numeric/bvp/convertsys) unable to convert to an explicit first-order system

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