## 10 Badges

19 years, 93 days

## How do I express bc for PDE...

Maple 2016

I have a PDE with boundary conditions, from a NASA paper.  I always seem to have problems expressing the bc.

PDE := diff(u(x, t), t) = (1/4)*exp(2)*exp(-u(x, t))*(diff(diff(u(x, t), x), x))/(x^2+2);

The initial/boundary conditions are

@t=0, u(x, t) = 2-2*ln(-x^2+2)

@x=0, diff(u(x,t),x)=0  ## this is the bc I have problem expressing

@x=1, u(x,t) = 2+ln(1+t)

The exact solution given in the paper:

2 + ln(1+t) - 2*ln(2-x^2)

I tried

ics := u(x, 0) = 2*(1-ln(2-x^2));

bcs := D[1](u(0,t))=0, u(1,t)=2+ln(1+t);

PDEtools[Solve]([PDE,ics,bcs]); ## no solution

How do I do this?

Tom Dean

## How do I put discussions, mixed with exe...

Maple

I have several maple worksheets (from the web) that have discussion blocks mixed within executable blocks.

All the executable blocks are delineated with a single '[' at the left while the discussion blocks do not.

How do I do this?

Tom Dean

## Geometric Proof...

Maple 2016

I attempted to show that two lines are parallel.  I started with a problem in Geometry for which I do not have the solution.

I tried several ways with Maple to show this to be true.  Most of the time, I ended when maple could not determine if a-b = c-d, etc.

brg_proof.txt contains a statement of the problem and my latest maple code.

Question: How should I approach the proof, by the compass and straight edge method?  Is this possible in maple?

## Geometry Intersection Fails...

Maple 2016

intersection in the geometry package does not seem to recognize assume.

restart: with(geometry):

assume(p[1]<>0, p[2]<>0, p[3]<>0);
assume(q[1]<>0, q[2]<>0, q[3]<>0);
point(T,[p[1],q[1]]);
point(U,[p[2],q[2]]);
point(V,[p[3],q[3]]);
point(Op,[0,0]);

line(OT,[Op,T]);
line(OU,[Op,U]);
line(OV,[Op,V]);

point(B,2*q[2],solve(subs(x=2*q[2],Equation(OU)),y));
coordinates(B);
IsOnLine(B,OU);

PerpendicularLine(AD,B,OT);
ArePerpendicular(AD,OT);
sol:=solve({Equation(AD),Equation(OT)},{x,y});
eval(x,sol);
point(A,eval(x,sol),eval(y,sol));  ## the intersection exists
intersection(xA,AD,OT); ## fails
about(p[1]),about(q[1]);

## Extracting View from Several Plots...

Maple 2016

I have several plots generated with geometry objects:

plt1 := draw(...); plt2 := draw(...)

I want to display all them with a reasonable window.  I have been looping and and using a rather dumb proc to find the window size. I use the view=[...] option with the values calculated to set the plot view.

I wanted to post the proc, but, really messed that up!  I will try the proc later.

Some of the plots I am working with have views like

> for itm in [relBrgLinePlot,relTgtPositPlot,relTgtLinePlot] do
op(-1,itm);
end do;
VIEW(0. .. 95., -61.58179461 .. 16.)
VIEW(5.48225506 .. 95., -61.58179461 .. 16.)
VIEW(5.48225506 .. 95., -61.58179461 .. 16.)

> for itm in [geoSensPositPlot,geoSensLinePlot,\
geoBrgLinePlot,geoTgtPositPlot,geoTgtLinePLot] do
op(-1,itm);
end do;
VIEW(0. .. 35.35331852, 0. .. 87.13244438)
VIEW(0. .. 35.35331852, 0. .. 87.13244438)
VIEW(0. .. 95., 0. .. 87.13244438)
VIEW(40.83557358 .. 95., 16. .. 25.55064977)
VIEW(40.83557358 .. 95., 16. .. 25.55064977)

Is there an easier way to do this?

 First 10 11 12 13 14 15 Page 12 of 15
﻿