## Maple Conference – New Deadline for Submissions

by: Maple Maple Toolboxes

I just wanted to let everyone know that the Call for Papers and Extended Abstracts deadline for the Maple Conference has been extended to June 14.

The papers and extended abstracts presented at the 2019 Maple Conference will be published in the Communications in Computer and Information Science Series from Springer. We welcome topics that fall into the following broad categories:

• Maple in Education
• Algorithms and Software
• Applications of Maple

https://www.maplesoft.com/mapleconference/Papers-and-Presentations.aspx

Hope to hear from you soon!

## A finite difference scheme for the heat equation...

Maple
 I describe here a finite difference scheme for solving the boundary value problem for the heat equation for the unknown temperature subject to the boundary conditions and the initial condition   This finite difference scheme is designed expressly with the goal of avoiding differentiating the conductivity , therefore  is allowed to be nonsmooth or even discontinuous. A discontinuous  is particularly important in applications where the heat conduction takes place through layers of distinct types of materials.   The animation below, extracted from the worksheet, demonstrates a solution  corresponding to a discontinuous .  The limit of that solution as time goes to infinity, which may be calculated independently and exactly, is shown as a gray line.

## i want to take export numbers from for loops in ma...

i wnat to take this export numbers from for loops in the matrix
restart;
with(LinearAlgebra);
f(x) :=  3*x^2+1 :
for i by .5 to 3.5 do print(i, f(i)) end do;

same this pic

## How do I get approximate solutions of this inequal...

I want to get solutions (approximate solutions) of the inequality g(x) > 0. I tried.

```restart;
fprime := x-> (x-1)*(x-2)^2*(x-3)*(x-4);
f := unapply(simplify(int(fprime(x), x)), x);
g := unapply(expand(f(3*x+1)-x^3+3*x), x);
solve(g(x) > 0, x);```

I got

## How do I use Homotopy Perturbation Method to find ...

Please, I need to use Maple to solve Euler-Bernoulli Beam on Pasternak Foundation using Homotopy Perturbation Method.

The governing equation is

initial conditions are

the boundary condition is

The governing equation represents Euler-Bernoulli beam on a generalized Pasternak viscoelastic foundation under an
arbitrary distributed dynamic load. in which E, I , ρ ,A are the parameters of the beam, representing Young’s modulus of elasticity, moment of inertia, density and area of cross section, respectively. K,C and Gp are spring stiffness, damping coefficient, and shear coefficient of the foundation. Moreover, y(x, t) and F(x, t) are defined as the vertical deflection of the beam and the generic arbitrary dynamic loads, respectively, where the loads distribute along the x-axis and t is time.

I will appreciate anyone who can help me with a Maple solution.

Thank you.

## Inconsistently working if-statements within a proc...

Would anybody be able to explain to me why I had to rewrite this one baby-procedure that has an if-statement inside my larger procedure, so that I could get a later on if-statement to work? As best I can tell, they mean exactly the same thing.

Information that may be pertinent:

- The entire (overall) procedure worked without throwing any warnings prior to my adding this new if-statement.
- The if-statement itself worked perfectly fine on another worksheet, though I hadn't tested it inside a procedure.
- Commenting out the if-statement but retaining the interior commands led to the sheet compiling again, showing that it was in fact the presence of the if-statement causing the issue.
- When I commented out the offending baby-procedure that started throwing the warning, the sheet once again compiled.

if eval_size > 4 then Search(max(seq(eval_cont[i], i = 4 .. eval_size)), eval_cont); evals_pairlist := evals_pairlist[[1 .. 3, %]] fi:

The error I get, and its "positioning":

Error, invalid expression for inline function

## remove some errors...

Hello,

How I can remove some problems in my code.

I wrote it before in  software, but in some lines, I have some problems with it.

How I can change it in maple to run well?

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## write whlie loop ...

How should wirte a while loop for solve nonlinear equations by newton raphson method

## homotopy pertubation...

Hi guys,
I am trying write a code for homotopy perturbation, i have already generated the polynomial as you can see, i have also  solve for concentration equation since is not couple. But i have a lot of error massages for temperature, velocity and induced magnetic field. can some one please go through the code?

 >
 > PDEtools[declare](f(x),theta(x),u(x),w(x), prime=x):
 (1)
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 > f(x):=sum((p^(i))*f[i](x),i=0..N);
 (2)
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## Problem with system of equation?...

Hello,

I got some problems with command solve .

I have to solve 6 equations with 6 unknowns. The problem is that Maple solves this system in a wrong way - the values calculated by the command are bad. I would like to ask if there is any command in Maple while solving the equations that are responsible for possible approximations when solving equations.
In the attachment I will insert the code I used.

https://www.pastiebin.com/5ce6a1943f548

## How can i solve "which is not valid for its 2nd ar...

Hi freind,

Anybody knows what happen to this coding?

why this error happens? how can i fix it?

thank you!

## Edge thickness of arcs in DrawGraph...

Hi everyone,

I was wondering how I could modify the thickness of edges in a graph displayed as a Maple plot through DrawGraph. The point is, the graph comprises 100 vertices and 1000 edges. By default, edge thickness is set as 2 but due to the high number of edges I would like to set edge thickness to1 or even 0. How can I do so?

Here is an example with a random graph:

with(GraphTheory) : with(RandomGraphs) : G := RandomGraph(100, 1000) : DrawGraph(G)

Thank you very much

## Writing a code for nested matrices...

where

and .

Also,

```restart:
with(LinearAlgebra):
interface(rtablesize=20):
with(plots):
k:=2:M:=2:
Tm:=(t,m)-> 2*t*Tm(t,m-1)-Tm(t,m-2);
Tm(t,0):=1:
Tm(t,1):=t:

Tm2:=(tt,m)->subs(t=tt,Tm(t,m)):
alpha:=(m)->piecewise(m=0,1/sqrt(Pi),sqrt(2)/sqrt(Pi));
psii:=(n,m,x)->piecewise((n-1)/(2^(k-1)) <= x and x <= n/(2^(k-1)),
alpha(m)*(2^(k/2))*Tm2(2^k*x-2*n+1,m), 0);
psi:=(t)->Array([seq(seq(psii(i,j,t),j=0..M-1),i=1...2^(k-1))] ):
for i from 1 to ((2^(k-1))*M) do
r[i]:=evalf(psi((2*i-1)/((2^k)*M))):
end do:
m:=M*(2^(k-1)):
xi:=(i,n)->((i+1)^(n+1)-2*i^(n+1)+(i-1)^(n+1));
PB_n:=Matrix(m,m)

```

Could you help me to complete the code?

Best regards.

## Bug When Using IntegrationTools[Change] With Assum...

Good day,

I was recently using Maple 2019 for work on a project, and ran into an error. This error (which will be copied and pasted below for others to test) occurs when making assumptions across multiple lines (whether using the additionally function or not) while using IntegrationTools[Change]. It seems that, if during the process a variable that was within both the assumptions is subtracted from itself, the subtraction fails to happen and leaves what effectively equals 0 in the workings, making further workings impossible.

I'm wondering if anyone else is able to reproduce this error? I know the fix for it is to not disjoint the assumptions, but I am curious if others can easily reproduce it or if others have experiences with it!

As promised, below you will find my workings in order to reproduce this error!

Base Error:

restart;
assume(a>0,b>0,b>a,c>0,t>0);
interface(showassumed=0);
F := Int(sqrt(d-a*c^2*t),d=0...infinity);
assume(b>a);
IntegrationTools[Change](F,-a*t*c^2+d=-y,y)

Simple Fix:

restart;
assume(a>0,b>0,b>a,c>0,t>0);
interface(showassumed=0);
F := Int(sqrt(d-a*c^2*t),d=0...infinity);
IntegrationTools[Change](F,-a*t*c^2+d=-y,y)

Error Without Interface Change:

restart;
assume(a>0,b>a,c>0,t>0);
F := Int(sqrt(d-a*c^2*t),d=0...infinity);
assume(b>a);
IntegrationTools[Change](F,-a*t*c^2+d=-y,y)

restart;
assume(a>0,b>a,c>0,t>0);
interface(showassumed=0);
F := Int(sqrt(d-a*c^2*t),d=0...infinity);
IntegrationTools[Change](F,-a*t*c^2+d=-y,y)

## fix simplify problem...

restart;
lambda := 1;
1
mu := 1;
1
alpha := 1;
1
v := 2;
2
delta := 1;
1
m := 1;
1
d := 3;
3
l := 1;
1
omega := -(1/2)*a*lambda^2-a*m^2+2*a*mu*v-delta*l*m-(1/2)*delta*lambda^2+2*delta*mu*v-l^2*mu-(1/2)*lambda^2*mu+2*mu^2*v-2*a*mu-2*delta*mu-2*mu^2;
1
- a + 1
2
a[0] := ((2*d*v-2*d-lambda)*(1/2))*sqrt(2)*sqrt(gamma*(a+delta+mu))/gamma;
(1/2)                (1/2)
5 2      (gamma (a + 2))
-----------------------------
2 gamma
a[1] := 0;
0
a[2] := -(2*(1/2))*sqrt(2)*sqrt(gamma*(a+delta+mu))*(d^2*v-d^2-d*lambda+mu)/gamma;
(1/2)                (1/2)
7 2      (gamma (a + 2))
- -----------------------------
gamma
Omega := lambda^2-4*mu*v+4*mu;
-3
H := (-lambda+sqrt(-Omega)*tan((1/2)*sqrt(-Omega)*xi))/(2*(v-1));
1   1  (1/2)    /1  (1/2)   \
- - + - 3      tan|- 3      xi|
2   2           \2          /
u := a[0]+a[1]*(d+H)+a[2]/(d+H);
(1/2)                (1/2)
5 2      (gamma (a + 2))
-----------------------------
2 gamma

(1/2)                (1/2)
7 2      (gamma (a + 2))
- -------------------------------------
/5   1  (1/2)    /1  (1/2)   \\
gamma |- + - 3      tan|- 3      xi||
\2   2           \2          //

eta := -l*y-m*x+omega*t;
/1      \
-y - x + |- a + 1| t
\2      /
u := a[0]+a[1]*(d+H)+a[2]/(d+H);
(1/2)                (1/2)
5 2      (gamma (a + 2))
-----------------------------
2 gamma

(1/2)                (1/2)
7 2      (gamma (a + 2))
- -------------------------------------
/5   1  (1/2)    /1  (1/2)   \\
gamma |- + - 3      tan|- 3      xi||
\2   2           \2          //

f := diff(u, xi);
/                      2\
(1/2)                (1/2) |3   3    /1  (1/2)   \ |
7 2      (gamma (a + 2))      |- + - tan|- 3      xi| |
\4   4    \2          / /
-------------------------------------------------------
2
/5   1  (1/2)    /1  (1/2)   \\
gamma |- + - 3      tan|- 3      xi||
\2   2           \2          //
S := diff(u, xi);
/                      2\
(1/2)                (1/2) |3   3    /1  (1/2)   \ |
7 2      (gamma (a + 2))      |- + - tan|- 3      xi| |
\4   4    \2          / /
-------------------------------------------------------
2
/5   1  (1/2)    /1  (1/2)   \\
gamma |- + - 3      tan|- 3      xi||
\2   2           \2          //
xi := x+y-(-2*alpha*m-delta*l-delta*m-2*l*mu)*t;
x + y + 6 t
eq := (-omega-a*m*m-delta*l*m-mu*l*l)*u-(gamma*u*u)*u+(a+delta+mu)*S;
/   (1/2)                (1/2)
/  3      \ |5 2      (gamma (a + 2))
|- - a - 3| |-----------------------------
\  2      / |           2 gamma
|
\

(1/2)                (1/2)          \         /
7 2      (gamma (a + 2))               |         |
- ------------------------------------------------| - gamma |
/5   1  (1/2)    /1  (1/2)              \\|         |
gamma |- + - 3      tan|- 3      (x + y + 6 t)|||         |
\2   2           \2                     ///         \

(1/2)                (1/2)
5 2      (gamma (a + 2))
-----------------------------
2 gamma

(1/2)                (1/2)          \
7 2      (gamma (a + 2))               |
- ------------------------------------------------|^3 +
/5   1  (1/2)    /1  (1/2)              \\|
gamma |- + - 3      tan|- 3      (x + y + 6 t)|||
\2   2           \2                     ///

/
1                         |
------------------------------------------------- |7 (a + 2)
2 \
/5   1  (1/2)    /1  (1/2)              \\
gamma |- + - 3      tan|- 3      (x + y + 6 t)||
\2   2           \2                     //

/                                 2
(1/2)                (1/2) |3   3    /1  (1/2)              \
2      (gamma (a + 2))      |- + - tan|- 3      (x + y + 6 t)|
\4   4    \2                     /

\\
||
||
//
value(%);
/   (1/2)                (1/2)
/  3      \ |5 2      (gamma (a + 2))
|- - a - 3| |-----------------------------
\  2      / |           2 gamma
|
\

(1/2)                (1/2)          \         /
7 2      (gamma (a + 2))               |         |
- ------------------------------------------------| - gamma |
/5   1  (1/2)    /1  (1/2)              \\|         |
gamma |- + - 3      tan|- 3      (x + y + 6 t)|||         |
\2   2           \2                     ///         \

(1/2)                (1/2)
5 2      (gamma (a + 2))
-----------------------------
2 gamma

(1/2)                (1/2)          \
7 2      (gamma (a + 2))               |
- ------------------------------------------------|^3 +
/5   1  (1/2)    /1  (1/2)              \\|
gamma |- + - 3      tan|- 3      (x + y + 6 t)|||
\2   2           \2                     ///

/
1                         |
------------------------------------------------- |7 (a + 2)
2 \
/5   1  (1/2)    /1  (1/2)              \\
gamma |- + - 3      tan|- 3      (x + y + 6 t)||
\2   2           \2                     //

/                                 2
(1/2)                (1/2) |3   3    /1  (1/2)              \
2      (gamma (a + 2))      |- + - tan|- 3      (x + y + 6 t)|
\4   4    \2                     /

\\
||
||
//

simplify(%);
Error, (in simplify/tools/_zn) too many levels of recursion

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