Hi everybody,

i'm trying to do an elliptic regularization but i don't know how to proceed ?

Is someone know how to achieve to do that  with an example ?

thanks a lot !

PS: i know only how to do a linear regularisation.

I am considering the following PDE and I am getting an error, please suggest a better numerical method than the default one used in maple:

the PDE is:

u_{xx}u^3 - sin(xt)u_{tt} = u(x,t)

u(x, 0) = sin(x), (D[2](u))(x, 0) = cos(x), u(0, t) = cos(t), (D[1](u))(0, t) = sin(t)

Please suggest me a method that will also work for the following PDEs:

u^m* u_{xx} - sin(xt)u_{tt} = u^n

for m,n =0,1,2,3,... for the cases m=n and m not equal n

Here's the code:

Download nonlinear_hyperbolic_PDE.mw

HI there,

I m getting an error message . Could someone help me

v1 := int(cos(tau)*g(tau), tau = t0 .. t);
int(cos(tau) g(tau), tau = t0 .. t)
v2 := int(-sin(tau)*g(tau), tau = t0 .. t);
int(-sin(tau) g(tau), tau = t0 .. t)
soln := C1*y1+C2*y2+v1*y1+v2*y2;
C1 y1 + C2 y2 + (int(cos(tau) g(tau), tau = t0 .. t)) y1

+ (int(-sin(tau) g(tau), tau = t0 .. t)) y2
soln := combine(soln);
(int(-y2 sin(tau) g(tau) + y1 cos(tau) g(tau), tau = t0 .. t))

+ C1 y1 + C2 y2
eval(soln, t = t0) = 0, eval(diff(soln, t), t = t0);
C1 y1 + C2 y2 = 0, -y2 sin(t0) g(t0) + y1 cos(t0) g(t0)
solve({%}, {C1, C2});
soln := eval(soln, %);
Error, invalid input: eval received (C1*y1+C2*y2 = 0, -y2*sin(t0)*g(t0)+y1*cos(t0)*g(t0)), which is not valid for its 2nd argument, eqns

Is there a maple function that'll allow me to generate the matrix M(5 by 5) below given that matrix A and B are 3 by 3 M:=LinearAlgebra:-ZeroMatrix(5) A:=Matrix([[a11,a12,a13],[a21,a22,a33],[a31,a32,a33]]) B:=Matrix([[b11,b12,b13],[b21,b22,b33],[b31,b32,b33]]) Matrix(5, 5, {(1, 1) = a[11], (1, 2) = a[12], (1, 3) = a[13], (1, 4) = 0, (1, 5) = 0, (2, 1) = a[12], (2, 2) = a[22], (2, 3) = a[23], (2, 4) = 0, (2, 5) = 0, (3, 1) = a[13], (3, 2) = a[23], (3, 3) = a[33]+b[11], (3, 4) = b[12], (3, 5) = b[13], (4, 1) = 0, (4, 2) = 0, (4, 3) = b[12], (4, 4) = b[22], (4, 5) = b[23], (5, 1) = 0, (5, 2) = 0, (5, 3) = b[13], (5, 4) = b[23], (5, 5) = b[33]});

Just purchased Maple 2015 and playing with it for the first time.  I'm running the 64-bit version on Win 8.1.

Anytime the program generates a pop-up dialog box, the pop-up seems to get stuck behind the main program window.  I can't alt+tab to get to the pop-up window and I can't click on anything in the main program window because it's frozen while waiting for me to aknowledge the pop-up dialog box.  So I have to kill everything from the task manager and lose anything that's unsaved.

I'm talking about pop-ups for things like "Error, (in @@) invalid arguments"... I click on the link and see a brief flash while that pop-up quickly flies behind the main window.  Same thing happens when I click on a link that asks what web browser I want to use.

I can't be the only one that has this problem, so is there a fix or workaround for this somewhere?  It's not really useable like this.  Thanks!

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