Melvin Brown

74 Reputation

3 Badges

13 years, 128 days

Social Networks and Content at Maplesoft.com

Maple Application Center

MaplePrimes Activity


These are questions asked by Melvin Brown


I am unable to replicate solution of problem 169 below.  Can you help me debug?

Melvin Brown

Schrdiff(o(t), t, t)dinger PDE on (x,y,t) with initial and boundary conditions. Zero potential: problem number 169

 

Here is the problem 169 specification and solution from the Nasser list:

restart

with(PDEtools); with(CodeTools)

x:='x';t:='t';y:='y';hbar:='hbar';

x

 

t

 

y

 

hbar

(1.1)

interface(showassumed=0);

1

(1.2)

pde:=I*diff(f(x,y,t),t)=-hbar^2*(diff(f(x,y,t),x$2)+diff(f(x,y,t),y$2))/(2*m);

I*(diff(f(x, y, t), t)) = -(1/2)*hbar^2*(diff(diff(f(x, y, t), x), x)+diff(diff(f(x, y, t), y), y))/m

(1.3)

ic:=f(x,y,0)=sqrt(2)*(sin(2*Pi*x)*sin(Pi*y)+sin(Pi*x)*sin(2*Pi*y));

f(x, y, 0) = 2^(1/2)*(sin(2*Pi*x)*sin(Pi*y)+sin(Pi*x)*sin(2*Pi*y))

(1.4)

bc:=f(0,y,t)=0,f(1,y,t)=0,f(x,1,t)=0,f(x,0,t)=0;

f(0, y, t) = 0, f(1, y, t) = 0, f(x, 1, t) = 0, f(x, 0, t) = 0

(1.5)

cpu_time := timelimit(60*10,CodeTools[Usage](assign('sol',pdsolve([pde,ic,bc],f(x,y,t))),output='realtime'));

memory used=159.58MiB, alloc change=102.00MiB, cpu time=4.37s, real time=4.23s, gc time=452.40ms

 

4.233

(1.6)

with(plots); evalf(f(1, 2, 2))

f(1, 2, 2)

(1.7)

plot3d(f(x, y, 3), x = -1 .. 1, y = -1 .. 1)

Warning, expecting only range variables [x, y] in expression f(x,y,3) to be plotted but found name f

 

 

The problem seems to fail... Why?

``


 

Download TestCaseforMapleStaff.mw

I get the following when MAPLE starts...

Warning, .hdb help databases are deprecated, 'C:\Program Files\Maple 2018\lib\OrthogonalExpansions.hdb' will not be used, see ?HelpTools,Migrate help page for more information

I have recently loaded an orthogonal expansions package created for earlier versions of MAPLE.

How can I remove the message?

MRB
 

Does MAPLE have capabability to do multidimensional FTs i.e. (x,y)->(u,v)? If not, are there any links to MAPLE packages which meet this requirement that can be recommended?

Melvin Brown

 

 

Dear Support

I am attempting to model quantum dynamics, and have defined a coupled set of nonlinear PDEs I would like to solve for coupled solutions u(x,y,t) and v(x,y,t) using MAPLE 18.

I attach an image of part of the worksheet the pair of PDEs...The initial conditions u(x,y,0), v(x,y,0) are a pair of respectively positive and negative 2D gaussians on the x,y, domain.

Before I go any further, please would you check that MAPLE 18 is in principle capable of finding solutions u(x,y,t), v(x,y,t) solutions, and let me know whether it is worth pursuing the solution?  I have had a look at the MAPLE documentation, but am not sure whether MAPLE can solve this system.

As a warm-up, I successfully solved a 1-D system u(x,t), v(x,t) using pdsolve[numeric], but I am not clear whether MAPLE 18 can solve for u(x,y,t), v(x,y,t) either numerically or analytically on the [x,y,t] domain.

I hope you can provide help/guidance. An image the equations in MAPLE is displayed here...

Melvin Brown

UK

I understand that Maple 2018 is now able to solve 3 independent variable PDE & BC problems in bounded domains through separation of variables by product and eigenfunction expansion.

My solution domain is (x,y,t), (i.e three independent variables) but I would like to need to use numerical integration.  Are there plans to make numerical integration for PDEs with three independent availables, and if so when is that facility likely to be available?

Melvin

 

 

1 2 3 4 5 6 Page 1 of 6