javid basha jv

## 8 Badges

6 years, 185 days

## Thank you, derivatives are not executing...

Dear @tomleslie

Thanks for your help.

I am glad for your reply.

I am using the maple 18 version. In this, the first and second derivatives are not executing. Kindly help me to rectify the issue.pdeTut_(2).mw

 > restart:
 > ra:=2: b1:=1.41: na:=0.7: we:=0.5: eta[1]:=4*0.1: d:=0.5/1:   xi:=0.1: m:=na: ea:=0.5: pr:=21: gr:=0.1: R:=0.9323556933:
 > PDE1:=ra*(diff(f(x,t),t))=+b1*(1+ea*cos(t))+(1/(R^2))*((diff(f(x,t),x,x))+(1/x)*diff(f(x,t),x));   IBC:= {D[1](f)(0,t)=0,f(1,t)=0,f(x,0)=0};
 (1)
 > # # Solve the PDE then use the returned methods 'plot', 'plot3d', # and 'animate' to produce various plots #   sol :=  pdsolve({PDE1}, IBC, numeric) :   sol:-plot(f(x, t), t = 1.2, linestyle = "solid", title = "Velocity Profile", labels = ["r", "f"]);   sol:-plot3d(f(x, t), x=0..1, t=0..2, style=surface, color=cyan );   sol:-animate( f(x,t), x=0..1, t=0..2);
 > # # Use the 'value' method to facilitate computation of # assorted numerical values # # Check which quantities are "immediately available" #   sol:-value(f(x,t), output=listprocedure); # # Aow get some numerical values from this basic method #   sol:-value(f(x,t))(0.5,0.5); # # For ease of use, one can assign the 'f(x,t)' procedure to, # the name 'fN' and then compute the values, as in #   fN:=eval( f(x,t), sol:-value(f(x,t), output=listprocedure)):   fN(0.5,0.5);
 (2)
 > # # The solution module returned by pdsolve() does not # contain any derivatives, so these have to be computed # explicitly. The simplest method is to use the 'D' # operator. # # Differentiation wrt 'x' evaluated at x=0.2, t=1.2 #   D[1](fN)(0.2, 1.2); # # Differentiation twice wrt 'x' and evaluate at x=0.2, # t=1.2 #   D[1,1](fN)(0.2, 1.2); # # Differentiation wrt 't' evaluated at x=0.2, t=1.2 #   D[2](fN)(0.2, 1.2); # # Plot the first and second derivatives of f(x,t) wrt 'x' for t=1.2 # Note the "glitch" in the second derivative #   plot( [ D[1](fN)(x, 1.2),           D[1, 1](fN)(x, 1.2)         ],         x=0..1,         color=[red, blue]       ); # # Plot the first and second derivatives of f(x,t) wrt 't' for x=0.5 #   plot( [ D[2](fN)(0.5, t),           D[2, 2](fN)(0.5, t)         ],         t=0..2,         color=[red, blue],         axes=boxed       );
 > M:= Matrix([ [ "x", "f(x,t)", "diff(f(x,t),x)", "diff(f(x,t),x,x)"],                   seq( [j, fN(j, 1.2), D[1](fN)(j,1.2), D[1,1](fN)(j,1.2)], j=0.1..0.9, 0.1)                ]             );  # ExcelTools:-Export( M, "C:/Users/TomLeslie/Desktop/pdeDat.xlsx")
 (3)
 >

 > restart:
 > ra:=2: b1:=1.41: na:=0.7: we:=0.5: eta[1]:=4*0.1: d:=0.5/1:   xi:=0.1: m:=na: ea:=0.5: pr:=21: gr:=0.1: R:=0.9323556933:
 > PDE1:=ra*(diff(f(x,t),t))=+b1*(1+ea*cos(t))+(1/(R^2))*((diff(f(x,t),x,x))+(1/x)*diff(f(x,t),x));   IBC:= {D[1](f)(0,t)=0,f(1,t)=0,f(x,0)=0};
 (1)
 > # # Solve the PDE then use the returned methods 'plot', 'plot3d', # and 'animate' to produce various plots #   sol :=  pdsolve({PDE1}, IBC, numeric) :   sol:-plot(f(x, t), t = 1.2, linestyle = "solid", title = "Velocity Profile", labels = ["r", "f"]);   sol:-plot3d(f(x, t), x=0..1, t=0..2, style=surface, color=cyan );   sol:-animate( f(x,t), x=0..1, t=0..2);
 > # # Use the 'value' method to facilitate computation of # assorted numerical values # # Check which quantities are "immediately available" #   sol:-value(f(x,t), output=listprocedure); # # Aow get some numerical values from this basic method #   sol:-value(f(x,t))(0.5,0.5); # # For ease of use, one can assign the 'f(x,t)' procedure to, # the name 'fN' and then compute the values, as in #   fN:=eval( f(x,t), sol:-value(f(x,t), output=listprocedure)):   fN(0.5,0.5);
 (2)
 > # # The solution module returned by pdsolve() does not # contain any derivatives, so these have to be computed # explicitly. The simplest method is to use the 'D' # operator. # # Differentiation wrt 'x' evaluated at x=0.2, t=1.2 #   D[1](fN)(0.2, 1.2); # # Differentiation twice wrt 'x' and evaluate at x=0.2, # t=1.2 #   D[1,1](fN)(0.2, 1.2); # # Differentiation wrt 't' evaluated at x=0.2, t=1.2 #   D[2](fN)(0.2, 1.2); # # Plot the first and second derivatives of f(x,t) wrt 'x' for t=1.2 # Note the "glitch" in the second derivative #   plot( [ D[1](fN)(x, 1.2),           D[1, 1](fN)(x, 1.2)         ],         x=0..1,         color=[red, blue]       ); # # Plot the first and second derivatives of f(x,t) wrt 't' for x=0.5 #   plot( [ D[2](fN)(0.5, t),           D[2, 2](fN)(0.5, t)         ],         t=0..2,         color=[red, blue],         axes=boxed       );
 > M:= Matrix([ [ "x", "f(x,t)", "diff(f(x,t),x)", "diff(f(x,t),x,x)"],                   seq( [j, fN(j, 1.2), D[1](fN)(j,1.2), D[1,1](fN)(j,1.2)], j=0.1..0.9, 0.1)                ]             );  # ExcelTools:-Export( M, "C:/Users/TomLeslie/Desktop/pdeDat.xlsx")
 (3)
 >

Download pdeTut_(2).mw

## I hope anyone may be reply...

Dear maple users,

Greetings.

I think the computation generates real and complex values.
How to plot only real numbers.

p1:= sol:-plot(R(z),t = 0, numpoints = 50);
NULL;
Error, (in pdsolve/numeric/plot) unable to compute solution for t<HFloat(0.0):
unable to store -.800000000000000e-4*2^(3/10)*((HFloat(undefined)+HFloat(undefined)*I)*2^(7/10)+437788563.900000*2^(3/10)+HFloat(undefined)+HFloat(undefined)*I)/(2*2^(3/10)+HFloat(undefined)+HFloat(undefined)*I)^2 when datatype=float[8]

I was waiting for at least anyone reply.

Have a good day

Javid Basha.

## Thank you...

Dear @mmcdara

Thanks for your help, The results are looking very nice.

## I hope it helps me...

Thank you very much for your effort.

I hope it helps me to update the graph.

Once again thanks a lot for your effort.

## Contour labels in the graph...

Is this possible to add contour labels to the graph?

Tim Leslie 7597  suggested the above-mentioned link,  there it is explained for algebraic functions only.

In this case, we have the data in the matrix form.

Kindly help me to shoot out this problem.

## How to add the labels in the graph...

Dear @tomleslie

Thanks for your reply.

Is this possible to add the contour sequence and how to incorporate the labels in the graph?

## How to get the solution...

Dear @tomleslie

Is there any possibility to get a solution to this problem?
Waiting for your reply.

## Please find this attachment....

Dear @tomleslie

Please find this attachment.
This paper problem only I am trying to get a solution.

Paper: perturbation.pdf

In this paper, equations 14-16 are solved using the perturbation function 20a-20e with the help of 17a, 17b and 18.

After applying the boundary condition and perturbation function in equations 14-16, they displayed the final form in equations 21-23.

## Results are not matching....

I have tried the below-mentioned problem. But the outcomes are not matching. I don't know where the mistakes happen.

Equation:

Condition:

perturbation expansion:

Outcome:

Result:

## Solution for this PDE Via Perturbation...

Is there any possibility to get a solution to this problem?
Waiting for your reply.

## Nice outcome....

Dear @tomleslie

The outcome looking good.
Thanks for your wonderful support.

## Thanking you for your attention...

Dear @tomleslie

Thanks for your notable support.

The outcome looking nice.

How to find values for R(0..1)

Only one point the value is coming.

X1[L[k]]:=rhs(R[L[k]](0..1)[4]);

## Thanks for the response....

Dear @tomleslie

I have applied sequences for "ax "
But solution is not coming.

How to get a result for the sequence of values.

## Waiting for your reply...

Dear maple users,
I hope anyone of the users answers this question.

## Thanks for the response....

Dear @Kitonum

Thanks for your reply.

And many thanks for your support.

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