## 74 Reputation

13 years, 282 days

## Problem with IBCs being rejected: for t...

Maple

I am trying to solve a coupled pair of PDEs (Burgers eqns) for u(x,t) and v(x,t).  However, my ICs and BCs are being rejected at the (0,0) corner of the domain.

PDE_rejects_IBCs.mw

Melvin

## Solving two coupled PDEs which have co...

Maple 2018

I am having problems with the attached worksheet, in which I am attempting to solve a couple pair of PDEs, particularly in defining initial and boundary conditions.  See MapleExample1c.mw

Can anyone help?

Melvin

## Graphical projection question: Projectin...

Can someone help me project ODE solution curves of an ODE onto velocity manifolds (u(x,t), v(x,t))?

Thanks for any help..

Melvin

Help needed to graphically map (x(t), t) trajectories onto velocity manifolds (u, v)

MRB: 16/6/19

The velocity manifolds u(x,t), v(x,t) are depicted in the figure below:

 >

The above velocity plot above shows classical pairs of negative (red) low and high velocity, and pairs of positive (blue) low and high velocity.  At any given instant there are fast and slow propagating solutions, from which classical trajectories on (x,t) are derived below for each of the red and blue velocity pulse solutions.  The cut away regions of the velocity manifolds represent complex  and

We now solve the velocity ODE to plot a (x,t) trajectory on the red velocity manifold:

 >
 >
 (1)

If the set of dependent variables is specified as a list, those variables appear in the same order in the output.  Now extract the solution points at given times

 >
 (2)

Here is a solution at a specified time:

 >
 (3)

Here is the the solution for the (x,t) trajectories:

 >
 (4)

We now plot trajectories on (x,t) space:

 >
 >

We do not generate trajectories in the region  for which regions of the manifolds are no longer real-valued.  The above trajectories are solutions of the above coupled Burger's equations for (u(x,t), v(x,t)). We wish plot these trajectories on their  [t,x(t),D(x(t)] manifolds.

 >

The following is an example of how to project curves onto a surface, assuming an analytic form for the curves.  However, we wish to project the above two ODE solution trajectory curves onto the surfaces u(x,t) and v(x,t) which are solutions of two PDEs.

Below is an example of projecting a specified curve onto a surface  Our requirement is to project a curve which is an integral solution of the ODE (4) above onto one of the velocity manifolds u(x,y), v(x,y).  Below is an example of an algebraically specified trajectory being projected onto a manifold (surface):

 >
 >
 (5)
 >
 >

QUESTION: We wish instead to project the ODE  (rather than algebraic) solution curves onto the surface.   Please someone provide MAPLE code to do that?

 >

## Can you help solution of the following P...

Maple

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

Melvin Brown

Schrdinger 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:

 >
 >
 > x:='x';t:='t';y:='y';hbar:='hbar';
 (1.1)
 > interface(showassumed=0);
 (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);
 (1.3)
 > ic:=f(x,y,0)=sqrt(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;
 (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
 (1.6)
 >
 (1.7)
 >

The problem seems to fail... Why?

 >

## How do I remove this message? ... Gener...

Maple

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

 1 2 3 4 5 6 Page 1 of 6
﻿