## Hardy-Littlewood maximal function of radial funct...

Dear all

I would like to compute Hardy−Littlewood maximal function : we use polar coordinate for a radial function  and then evalaute integral with respect the radius r

Hardy_maximal_function.mw

## limit at infinity ...

Dear all

I have an equation obtained from partial derivable of some functions, I would like to compute the limit when my variable named Pe goes to infinity.

I hope to get a more appreciate presentation of my code to obtain the limit (  Pe -> + infty)

limit_infinity.mw

All derivative are well compute, but How can I add the limit as Pe goes to infinity

Thank you

## number of arithmetic operations ...

Dear all

I construct by hand the two matrices L and U so that A= LU ( LU-factorization)
I would like to find the number of arithmetic operations required to obtain the matrices 𝐿 and 𝑈

Number_arithmetic_operation.mw

Thank you

## How to integrate the given function...

How to integrate the below function from 0 to eta.

A := P(eta)+S(H-2*`cos&theta;`(eta+1)*F)+`cos&theta;`*(2*F(eta)-2*H*F) = S(eta+1)*`sin&theta;`*F(theta)-`sin&theta;`(F*H(theta)-H*F(theta)+F(theta, eta))

## How to solve the given BVP using differential tran...

HI, I have numerically solved the given problem using the dsolve command But I want to solve the same problem using the Differential transformation method.
Can anyone help me to get the series solution for the given problem using DTM.

I want to compare the numerical results with DTM results when lambda =0.5.

eqn1 := diff(f(eta), `\$`(eta, 3))+f(eta)*(diff(f(eta), `\$`(eta, 2)))-(diff(f(eta), eta))^2-lambda*(diff(f(eta), eta)) = 0.

eqn2 := diff(theta(eta), `\$`(eta, 2))+f(eta)*(diff(theta(eta), eta))*Pr = 0

Bcs := (D(f))(0) = 1, f(0) = 0, (D(f))(infinity) = 0, theta(0) = 1, theta(infinity) = 0;

[lambda = .5, Pr = 6.3]

## fixed point method...

Dear all

I have a nonlinear system of algebraic equations, I would like to solve it  without using fsolve and Newton's method.
Maybe one can use, fixed point method or Broyden's method

Fixed_Broyden_method.mw

Can we solve the system of 4 equations, using the proposed methods

thank you

## Gauss seidel with chebychev acceleration ...

Dear all

I know how can I use gauss seidel to solve a linear system.

But, how can we add chebychev acceleration.

Thank you

## semi-numerical method versus exact solution...

Dear all

I compute the solution of first order nonlinear ode, supplied to initial condition.

The code is written, the exact solution is derived.

plot the solution in a small interval like (0,1/5) I see that there is no difference between exact and semi-analytical soluton.

But, If I plot the solution in other interval like (0,1) or (0,2), It is noticed that the semi-analytical solution is different to the exact solution.

test3.mw

## The Chaos Game and Generation of IFS...

Hi!

I have created a procedure for the so-called "Chaos Game" for the generation of Fractals. The file is the following:

Fractals_ChaosGame.mw

On the other hand, for a given day set D:={(x0,y0,(x1,y1),...., (xN,yN)}, for simplicity we assume D is contained in [0,1]x[0,1], one can to construct an "Iterated Functions System" such that its attractor set contains the set D. A detailed exposition of this topic can be found in the famous Barnsley's book "Fractals Everywhere". Also, in the following paper (sections 2.5 and 4-A):

https://arxiv.org/pdf/2102.09855.pdf

I have tried to implement in Maple 17 a procedure to create such Iterated Function System:

IFF_v2.mw

But, I feel that there is something wrong...After plot (with the Chaos Game procedure) a lot of points of the Iterated Functions System (i.e., an approximation of its attractor set), I have a "set of points", instead of a figure similar to a curve (which I feel that must be the correct).

Please, Somebody can have a look to the attached files?

## pde solve second order pde ...

Dear all

I have a second order PDE, i used pdesolve but no solution obtained, why?

pdsolve_pde.mw

thanks

## Maple using insert code edit region...

Dear all

I tried to used insert code edit region, to write many subcodes

but no return varibales names.

example, x:=3;

when I run the code, I get only the number affected to x, I would like to get

x:=3

No_return_variable.mw

Thank you

## How to draw a streamline by using stream function ...

How to draw a streamlines by using stream function provided in pdf. In the presence and absence of lambda parameter.

## trapezoid rule using loop...

Dear all

I tried to compute an integral using trapezoidal rule using two differents methods but I get two different results
trap.mw

## Why inequal plot like this?...

Hi there,

Can someone explain to me why is it happening? If smaller equal than coloured well, if smaller then just the equal line appears. Why?

```with(plots);
dm1 := .23; pm12 := .7; dm12 := .23;
inequal(pm1*(dm12+am21)-pm12*(dm1+am21) <= 0, pm1 = 0 .. 1, am21 = 0 .. 1, color = "Nautical 1");

```

`inequal(pm1*(dm12+am21)-pm12*(dm1+am21) < 0, pm1 = 0 .. 1, am21 = 0 .. 1, color = "Nautical 1")`

Thank you!

## Colouring inequalities...

Hello everyone,

I would have a question about how to colour a region of complicated inequalities.

I'm curious about the region where my 'lambdas' are all negatives regarding the parameters 'pm2' and 'am2', but I always find difficulties even if I try with implicitplot or inequal commands. Also, I would like to put into the same graph with different colours when they are separately smaller than 0.

I've already tried plenty of things, I hopefully attached some pics by snipping tool about them.  And here is an example of my problem:

`p61w:= implicitplot([lambda61 <= 0], pm2 = 0 .. 1, am2 = 0 .. 1)`

`in61 := inequal(lambda61 <= 0, pm2 = 0 .. 1, am2 = 0 .. 1)`

`display(in61,p61w)`

So, the main issue that it is not just coloured where my condition is true, but elsewhere too. In plot 'in61' as you can see, there is a region approx. pm2=0..0.6 where it shouldn't be coloured since my condition is not true there. In the graph; 'display(in61, p61w)',  it is visible that under the red line should be just coloured however my 'inequal' command coloured it outside too.

Also, I tried with implicitplot, for example:

`p6 := implicitplot([lambda61 <= 0], pm2 = 0 .. 1, am2 = 0 .. 1, filled = true, coloring = [blue, white], transparency = .5)`

But the result is similarly wrong. And I'm not sure why it happens and how can I fix it.

(It's okay if for example for these particular lambdas (lambda61,lambda62) never negatives together, but I have more systems and I don't think it works properly)

I read similar questions too but I couldn't find an answer so, I would very appreciate any suggestions.

This is my first post in Maple, so please let me know if I have mistaken something.

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