## solving a pde with boundary and initial conditions...

Hiya, I'm trying to solve this pde in Maple:

> PDE:= diff(c(z,t),t) = k*diff(c(z,t),z\$2) + w*diff(c(z,t),z);

where k, w are constants, but I don't know how to apply the boundary conditions:

c(0,t)=0 and 0=k*diff(c(z,t),z\$2) + w*diff(c(z,t),z) at z=h

and initial condition c=f(z) at t=0

I know by hand you would solve by separating variables, but is there an equivalent method in Maple?
Eventually I want to plot c(z) for given times to show how the solution evolves... but one thing at a time!

## How do I program a partial differential operator t...

Thank you everyone for all your help. However, what I am leading up to in my research requires that I overcome the following hurdle. Let p[m] represent an unspecified function of three variables, e1, e2, and e3. (In reality, the explicit formula for the function is known, but I will not use that formula.) m is an index. So, p[1], p[2], p[3] etc are different functions of e1, e2, e3. I need to program an operator, T, which acts on p[m] and returns - symbolically - T(p[m]) = 1*e1*diff(p[m],e1) + 2*e2*diff(p[m],e2) + 3*e3*diff(p[m],e3) In case anyone has guessed already, T has gone under such

## Labels on plot axes

by: Maple
The third example on the Plot Tickmarks and Gridlines help page - ?plot,tickmarks(tickmarks) - shows how to put labels at specific locations on a plot axis. But I couldn't find anything in the help pages about altering their font. However by changing the labels to names (enclose in left quotes, instead of double quotes) their font could be set using the axesfont option.

Perhaps something could be added to the example mentioned above. In the longer run though, all the help pages for plots need to be re-written: at present they resemble an untidy scrapbook.

J. Tarr

## effective sequence coding?...

What would be an effective way to code a sequence of numbers Y(t):=Poisson random variable with mean X(t) and X(t):=M+phi*X(t-1)+alpha*(Y(t-1)-X(t-1)) for 0<alpha<phi<1, M>0? Thanks.

## Phase potrait plot...

I am currently studying the phase portrait a differential equation: diff(y(t), t, t) = -piecewise((diff(y(t), t))*y(t) <><> 0 <><><> Initial conditions are: y(0) = 1; , diff(y(0), t) = 0; The phase portrait plots diff(y(t),t) with respect to y(t). I achieved the phase portrait using Simulink; with a few gain blocks, a switch and a X-Y scope, easily enough. When i was done, i wondered if i could analyze the equation with a more mathematical approach. I decided to try and plot the phase portrait using Maple 11. I have tried various commands to solve the differential equation with Maple 11 but so far i have confused myself.

## Contourplot bug

by: Maple
The command > contourplot(-1,x=0..1,y=0..1,contours=[0],filled=true); is supposed to fill the whole space with red (color for negative values) but it does nothing this is also problem once I need to define a piecewise function which is constant according to some condition, e.g. > f:=(x,y)->piecewise(x>1/2,x*y,-1); > contourplot(f(x,y),x=0..1,y=-1..1,contours=[0],filled=true); this should fill the entire half plane x>1/2 with red, it fills only part of the first quadrant...

## Problems with plotting user defined functions

by: Maple
The simpliest version of my problem is this: > f:=(x,y)->fsolve(sin(x+y+z)=1,z) > f(5,5); still ok but now: > plot(f(x,5),x=5..10); sais: "Error, (in fsolve) x is in the equation, and is not solved for" it seems as Maple would not first evaluate x:=5 and then solve f(x) :'(

## Solve parametric equations with restriction on par...

Hello! How can I solve a linear equation which depends on two parameters (a,b) for which the assumption a^2 + b^2 = 1 shall hold. This does not work by writing assume or assuming. The problem has the following form: tau := f(a,b) -> eigenvalues of a matrix U = U(a,b) M := U - tau*Id = M(tau,a,b) = M(a,b) find the kernel of M (eigenvectors of U) and simplify using a^2 + b^2 = 1. I do not want to write down the exact matrix and hope that this information is enough. If not, I will take some time to write it down. Greetings, yadaddy.

## How do I print?...

I have a Maple 11 Document and I'd like to print it. It currently has a couple graphs and text and mathematic equations on it. However, when I print the document the fonts are all jacked up. Minus signs show as vertical lines, fonts are on top of each other and it just looks terrible. I've tried exporting to HTML but the image quality is terrible on everything that wasn't entered as text. No apparent option to use anything but gifs which are the worst possible thing to use for quality. Any suggestions would be greatly appreciated. glenn

## equations: what they are, what they are not and wh...

This is a new thread to continue a discussion that started under the topic What is wrong with my program? (by resolvent). Here are the first three responses:

## How can I plot gridlines with 3d plot...

Does anybody know how can I plot 3D chart with gridlines for Axes style set to boxed? and the second question: How can I plot 3D chart with 3D bars?

## Conversion problem from matlab to maple...

Hi everyone, I am a new member of your group. I have a problem about matrix conversion from Matlab to Maple. In Matlab 7.0 i have created a program,this program sends a result matrix namely AT.This matrix is not symbolic, it is totally numeric. I would like to see this matrix inside of Maple 10. So far i could not make it. I would be grateful if you could help me. Greetings.