I want to solve numerically the PDE:

u_xx + u_yy= = u^{1/2}+(u_x)^2/(u)^{3/2}

My assumptions are that  |sqrt(2)u_x/u|<<1 (but I cannot neglect the first term since its in my first order approximation of another PDE.

So I tried solving by using pdsolve in maple, but to no cigar.

Here's the maple file:

 nonlinear.mw

Download nonlinear.mw

Hello All,

I looked through the Maple help on PDE systems and pdsolve and the physics problems that appear there. THere are a number of single-PDE cases with initial / boundary conditions; but I couldn't find PDE systems with ics/bcs.

Would you have a (simple) example of a PDE system with its initial / boundary conditions? I am attempting to build understanding of the syntax and different options of "pdsolve". Examples seem to be a great way to learn how to solve PDE systems. One can then pdsolve the PDE system without ics; then add them, try different options etc.

Thank you!

I have an arrays of data. One for x values, and one for y values. How can I obtain a numerical integration of y for a range of x values?

I have tried defining a function of X using ArrayInterpolation(x,y,X) and then calling evalf(Int(f,xmin..xmax)) but that gives an error message. (I don't seem to be able to paste into this window) The error message says

"Error, invalid input: evalf expects its 2nd argument, n, to be of type posint, but received numeric."

I thought I was using a form of the equation right from the help system.

I also tried the 2D version of integration, but it returns the difference of my limits times my function name.

I aslo tried AdaptiveQuadrature, but I can't get that to work either.

-Mike McDermott

Newbie Maple user

Hi,
I'm new at maple and have a problem/question with the rkf45 numerical ODE Solver.

At first, my computer need a lot of time to calculate an analytic solution.
Therefor, I use the numerical way.

I have the following second order ODE:
ODE:=m*((D@@2)(x))(t)+d*(D(x))(t)+k*x(t) = d*(eval(diff(y(x), x), x = t))+k*y(t)
where y(t) is a realy big piecewise function, defined by me.

My initial conditions are:
x(0) = 0, (D(x))(0) = 0

With dsolve, I get the solution x(t) and the first derivative x'(t). I'm able to plot them with odeplot.

But...

Problem 1:
I need also the second derivative x''(t).
On this page: http://www.maplesoft.com/support/help/maple/view.aspx?path=dsolve%2Frkf45there is an example (eq 13 and 14) where the second derivative is useable, but this doesn't work with my differential equation.
I have add 
(D(D(x)))(0) = 0
to my initial conditions but then, I got the error that only 2 initial conditions are required.
What could I do, so that rkf45 returns also the second derivative?

Problem 2:
And in addition to this, I want to calculate with x(t), x'(t), x''(t) but I found no way to use them.
Only plots are possible.
If I reduce y(t) to a minimum, I can do everything with the analytic solution: plot, d/dt, d2/dt2, +, -, ...
I tried also to convert the procedure to a function but in this case, there is no way to derivate it.

Many thanks...

Hi,

  My question is related to this one http://www.mapleprimes.com/questions/37447-How-Can-I-Sort-A-List-Of-List-According

but not exactly the same.

  Suppose I have lists

***

f[1]:=[1,3,2];
f[2]:=[2,1,3];
f[3]:=[1,2,3];
f[4]:=[2,3,1];
f[5]:=[3,2,1];
f[6]:=[3,1,2];

***

  The aim of sorting is first, arrange by ascending order of the first variable, then the second, then the third.

I could program manually by explicitly comparision, is there any robust way in maple can do it (possibly a few build-in function)?

Thank you very much!

Just trying Maple again after 10+ years, so please bear with me. I am basically trying to do a symbolic integration, where the output should be the antiderivative of the function I am integrating. However, I have not been able to succesfully get the output I expect.

I defined a function C_p(T), with constants C₁, C₂, etc. like so:

C__p := T -> C__1+C__2(C__3/(T*sinh(C__3/T)))^2+C__4(C__5/(T*cosh(C__5/T)))^2 

But when I integrate the function using int(C_p(T), T=T_ref..T_sys) it does not output the antiderivative as I would expect. This is what I am looking for, but it just gives me the equation within the integral sign without symbolically solving integral. Can this be done?

It should be,

int(C_p(T), T=T_ref..T_sys) = C₁*(T₂-T₁) + C₂*C₃[coth(C₃/T₂) - coth(C₃/T₁)] - C₄*C₅[tanh(C₅/T₂)-tanh(C₅/T₁)]

Trivial integrals such as int(x2,x) = 2x solve okay, so I am assuming I setup the problem incorrectly. I just cannot figure out what I did wrong, and it is driving me crazy. I already wasted more time than is healthy on this. Any help would be greatly appreciated. Thanks.

Hi,

I am trying to use implicit plot. The plot is OK but I want to put labels such as what Latex produces :

$\frac{\Omega}{\omega_n}$ for x axis and $a_0 \mathrm{(m)}$ for y axis

How can I apply this in my maple code as below:

plot1:=implicitplot(a3, Omega_r=1.5..2.5, a=0.00000001..0.1, labeldirections=[horizontal, horizontal], axes=boxed, labels=["W/w_n",typeset("a_0 (m)")], labelfont=[SYMBOL]):

What I have put as bold does not work for me, it is making everything in Greek :) . I want combination of Greek and math.

Thasnks,

Bahareh

In this work the theme of vector analysis shown from a computational point of view; this being a very important role in the engineering component; in civil and mechanical special it is why, using the scientific software Maple develops interactive solutions for long processes through MapleCloud calculations. At present the majority of professors / researchers perform static classes open source leaves; so that our students learn and memorize commands, thus generating more time learning in the area. Loading Bookseller VectorCalculus develop topics: vector algebra, differential operators, conservative fields, etc. Maplesoft making processes provide immediate calculations long operation Embedded Components displayed in line with MapleNet integrations. Today our future engineers to design solutions and will be launched in the cloud thus being a process with global qualification in the specialty. Significantly Maple is a scientific software which allows the researcher to design their own innovations and not use themes for their manufacturers.

III_CRF_2015.pdf

CRF_2015.mw

L.AraujoC.

I want to solve numerically the nonlinear pde:

u_x+u_t - (u_{xt})^2 = u(x,t)

which method do you propose me to use with maple? (I don't mine about which boundary conditions to be used here).

Hello.
Have a question for use Physics[TransformCoordinates] . For example, in a Cartesian coordinate system is an arbitrary tensor. As you know, in this case the covariant, contravariant and mixed components are the same. We have a coordinate transformation such as transforming our Cartesian coordinate system in the oblique coordinate system. In this simple example, correctly calculated the covariant, contravariant and mixed components (structure: covariant and contravariant), but other mixed components (structure: contravariant and covariant) are calculated is not correct. I checked by hand.

Download Transformation_tensor_components.mw

I recently got myself a 64 bit computer and have noticed that I cannot use the option compile=true in dsolve/numeric. Take the following simple example:

dsolve({diff(x(t),t)=x(t),x(0)=1},numeric,compile=true);
Error, (in dsolve/numeric/SC/preproc) unable to compile (rc=1), please try again, and if that fails verify your Windows compiler installation

I'm using Windows 10, but had the same problem with Windows 8.1 on the same machine.
The Compiler:-Compile examples in the help page all work.

What do I have to do to make the option compile=true work in dsolve/numeric?

You may safely assume that I don't know any technicalities about these things.

How to change the font style, globally, the inputs and outputs of computations in Maple 2015? That is, every time a new document is started, the chosen style is automatically applied.

Oliveira.

Hi,

  I have the following input in order to obtain the dimension of an array, by means of the values has been assigned

with(ArrayTools):
with(LinearAlgebra):
f[1]:=1:
f[2]:=2:
nops(f);
Size(f);
Dimension(f);

  The result is 

---

1
[ 1 1 ]
Error, invalid input: LinearAlgebra:-Dimension expects its 1st argument, A, to be of type {Matrix, Vector} or coercible via `~Simplify`, but received f

 ---

I cannot get number "2", which is expected. Is there any way to obtain that? I looked for help and mapleprime, without any simple solution ......

Thank you very much!