Hi Robert,

After making the variable change you suggested it iterates for longer time.. but the output seems to be sensitive to the spacestep ie the plot is different for the same time but calculated with different spacesteps?

Also does it matter that the spacestep is odd/even or any relationship to range? because when I make say for example spacestep=90, 91  I am able to iterate for much longer time for 91,...

Vish

Hi Robert,

After making the variable change you suggested it iterates for longer time.. but the output seems to be sensitive to the spacestep ie the plot is different for the same time but calculated with different spacesteps?

Also does it matter that the spacestep is odd/even or any relationship to range? because when I make say for example spacestep=90, 91  I am able to iterate for much longer time for 91,...

Vish

Dear Robert,

That seems like a very good suggestion. I imposed the BC D[1](Phi)(0,t) = 0 in the first place to tackle this singularity at the equation. but it seems that when I make these changes it goes away. I have not tried it yet on maple.. 

However I have a question. Why does maple ask for boundary conditions even for wellposed initial value problems that only needs initial conditions?

 Also if you please can look at the original problem I had, of which this is a branch post, I had to make the spacestep really small for it to match the same function at t=0 which I put in as initial condition. When I try to plot the solution at t=0 for large spacestep it differes significantly from the known function at t=0,, I find it bizzare why maple would change it in the process of solving it 

Thanks very much for your attention. Looking forward to your suggestions

Kind regards,

Vish

Dear Robert,

That seems like a very good suggestion. I imposed the BC D[1](Phi)(0,t) = 0 in the first place to tackle this singularity at the equation. but it seems that when I make these changes it goes away. I have not tried it yet on maple.. 

However I have a question. Why does maple ask for boundary conditions even for wellposed initial value problems that only needs initial conditions?

 Also if you please can look at the original problem I had, of which this is a branch post, I had to make the spacestep really small for it to match the same function at t=0 which I put in as initial condition. When I try to plot the solution at t=0 for large spacestep it differes significantly from the known function at t=0,, I find it bizzare why maple would change it in the process of solving it 

Thanks very much for your attention. Looking forward to your suggestions

Kind regards,

Vish

@Markiyan Hirnyk It works for t=0 and the plot is fine, thanks to your help, .. but when I put t=10 for example in the plot command it returns the error. see corrected_code4(t=10.mw

@Markiyan Hirnyk It works for t=0 and the plot is fine, thanks to your help, .. but when I put t=10 for example in the plot command it returns the error. see corrected_code4(t=10.mw

@Markiyan Hirnyk Hi Markiyan,

Now the two plots are very similar at t=0(when space step is 0.1). However I am unable to evolve this beyond t>0.29999 I get an error message as,

Error, (in pdsolve/numeric/plot) unable to compute solution for t>.299999999999999988:
Newton iteration is not converging

I would be grateful for your suggestions 

Thanks

Vish

@Markiyan Hirnyk Hi Markiyan,

Now the two plots are very similar at t=0(when space step is 0.1). However I am unable to evolve this beyond t>0.29999 I get an error message as,

Error, (in pdsolve/numeric/plot) unable to compute solution for t>.299999999999999988:
Newton iteration is not converging

I would be grateful for your suggestions 

Thanks

Vish

@Markiyan Hirnyk  Hi Markiyan,

when I decrease the spacestep the plots seem to converge.. thank a lot. I would like to point out that Piinitial is differentiable at r=1,2  even it's derivative with respect to r is differentiable.. only d^2/dr^2 Piinitial is continuous but not smooth..

Is time step the iteration in r that maple does. Can you please explain why it works now?

Vish

@Markiyan Hirnyk  Hi Markiyan,

when I decrease the spacestep the plots seem to converge.. thank a lot. I would like to point out that Piinitial is differentiable at r=1,2  even it's derivative with respect to r is differentiable.. only d^2/dr^2 Piinitial is continuous but not smooth..

Is time step the iteration in r that maple does. Can you please explain why it works now?

Vish

@Markiyan Hirnyk Hi Markiyan,

Sorry if I am interupting your work. but even when I run your corrected code I get different plots.. May be you have not spotted the difference since the ranges were different. Please can you see the attached file where I have specified the same ranges for both plots and the difference is obvious..

I am using maple 12 do you think this might be an internal bug..

Thanks for your help

regards,

Vishcorrected_code.mw

@Markiyan Hirnyk Hi Markiyan,

Sorry if I am interupting your work. but even when I run your corrected code I get different plots.. May be you have not spotted the difference since the ranges were different. Please can you see the attached file where I have specified the same ranges for both plots and the difference is obvious..

I am using maple 12 do you think this might be an internal bug..

Thanks for your help

regards,

Vishcorrected_code.mw

@Markiyan Hirnyk 

Dear Markiyan,

Sorry, My name is Vishagan.S.. I have attached the code with inital profile (Phi(r,0)=Piinitial) and it's plot ALSO with the output of the pde and the function plot at t=0 which should be the same as Piinitial.. I am really confused with this problem..

I grateful for your help.Thanks..

kind regards,

Vish

Plotsandpde.mw

@Markiyan Hirnyk 

Dear Markiyan,

Sorry, My name is Vishagan.S.. I have attached the code with inital profile (Phi(r,0)=Piinitial) and it's plot ALSO with the output of the pde and the function plot at t=0 which should be the same as Piinitial.. I am really confused with this problem..

I grateful for your help.Thanks..

kind regards,

Vish

Plotsandpde.mw

maple_code.mw

@Markiyan Hirnyk