## Problem with pdsolve/numeric...

Problem with pdsolve/numeric

Contextualizing:

I created a routine for solving a thermo-mechanical problem. The size of the spatial domain is a function of time and the thermo-mechanical behavior of the structure.

The solution is obtained by discretizing the time domain in n intervals. The thermo-mechanical responses are obtained at each time t[i] =t[i-1]+dt.

The material exhibits elastic and elastoplastic mechanical behavior and thus the problem was divided into two consecutive phases (phase 1 and 2).

The heat problem is nonlinear because the thermal properties are variable (termal conductivity, specific heat, and density).

The problem:

In phase 2, the pdsolve/numeric command returns an error for the solution of the heat conduction equation (equation called pde1). I believe this error is related to the derivative of thermal conductivity k(x1) (piecewise function).

I tested many alternatives (I wrote the pde1 equation in two different ways), I checked the routine many times and I don't understand the reason for the error. With each attempt, the command returns a different error.

Thanks for your attention and help.

Problem.mw

## How can i differentiate with dotted lines on my gr...

Please can someone help me out, have been trying for a very long time now on how to differentiate the lines on the graph.......please find attachment below and correct..................................................................

restart;
with(plots):
#
# Define the ODE system
#
odeSys:= { (diff(F(eta), eta, eta, eta))*(1+epsilon-alpha((diff(F(eta), eta, eta))^2))+F(eta)*(diff(F(eta), eta, eta))+S*(diff(F(eta), eta))-(1/2)*S*eta*(diff(F(eta), eta, eta))-(diff(F(eta), eta))^2-M*(diff(F(eta), eta)), (diff(theta(eta), eta, eta))*(1+R)-delta*(diff(F(eta), eta))^2-Pr((3/2)*S*theta(eta)+(1/2)*S*eta*(diff(theta(eta), eta))-2*(diff(F(eta), eta))*theta(eta)+F*(diff(theta(eta), eta)))};
#
# Define the first set of boundary conditions
#
bcs1:= { F(0) = 0, (D(F))(0) = 1, (D(F))(inf) = 0, theta(0) = 1, theta(inf) = 0
}:

RVals:=[0.1, 0.5, 1]:
for k from 1 by 1 to numelems(RVals) do
pList:=[ epsilon = 0.18, M = 0.5, S = 1.5, delta = 0.3, Pr = 1.5, alpha = 0.4, R = RVals[k],inf=1
]:
sol1[k]:= dsolve( eval
( union( odeSys, bcs1),
pList
),
numeric
);
od:
display
( [ seq
( odeplot
( sol1[i],
[eta, theta(eta)],
eta=0..2
),
i=1..numelems(RVals)
)
],
color = [red, green, blue],
title = typeset( theta(eta), " versus ", eta),
titlefont = [times, bold, 20]
);

## Differential Transform Method...

Could anyone help me out to convert the equation into differential transform method

## Identifying Series...

Hello,

My question is quite simple yet maybe a bit hard since I understand that messing around with series can lead to dead ends.

Given a certain general term, for instance sum(x^n/n!,n=0..infinity): Can Maple recognize which function does it come from (in case such analytic function is known)? in the example I would expect it to return exp(x).

Thank you very much.

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## Unstability of the eigenvectors of some general ma...

Good morning all.
Consider $A=[a_{i,j}]$, a $18\times 18$ matrix (for example); the integer entries are randomly chosen in $[[-5,5]]$ (for example). In general, $A$ has distinct eigenvalues.

I seek the eigen-elements of $B=Transpose(A^{-1})A$ with $10$ significand digits (for example); in general, $B$ is diagonalizable ($P^{-1}BP=D$, a diagonal complex matrix). I use the command $evalf(Eigenvectors(?))$.

Many randomized tests require working with hundreds of Digits. The worst one requires $629$ digits!! Moreover (in this test), when $Digits:=400$, the condition number of $P$ is $10^{118}$ and , with $Digits:=619$, the condition number drops to $376$.

I am surprised by this instability. In particular, this method seems to be unusable when $n=100$.
Does there exist a method (using maple) which allows to solve the problem without dragging behind me a multitude of digits ? (perhaps with iterations...)

## Difficulties with parallel programming...

I have to compute some linear programming calculations. I thought it would be a good idea to perform them employing a parallel code. However, much to my surprise, the parallel code is slower than the single-threaded one. I enclose a worksheet sketching both codes with an example. Would you please tell me what it could be wrong with my code?

## How do I remove this error ''Error, (in dsolve/nu...

Please can you help me in resolving this error?

Here is the codeOptimal_control_model_of_DF_and_LP_2.mw

## Problem with pdsolve and piecewise functions...

Hello,

I have a nonhomogeneous heat conduction problem, where the thermal conductivity, the density, and the specific heat of the
material are piecewise functions.

The thermal conductivity derivative has a discontinuity that causes a problem in the pdsolve command (see the first test).

To avoid this problem, I did a second test where the product rule was calculated directly.

Is there a better way to deal with this problem?

thank you

problem.mw

## How to simplify this?...

xE.mw

I integrate the expression maple but the result is large. How to furtherxE.mw reduce the size of the result? Also, what is dilog on maple?

## How to calculate this?...

, where  is a complex parameter,  is a real constant and, , then how to calculate |u|^{2} on maple?

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Hello there,

Here is a set

thanks

## How to avoid the white patches in figure....

Dear maple users,

Greetings.

When converting the maple figure into EPS format (for latex) which shows white patches.

How to avoid such patches.