## How does fsolve work?...

When using the built-in fsolve function to find the roots of a polynomial, how does exponentiation occur? For example, x3 is found​​​​​​first, and then to find x4, will he start again from the beginning, that is, x*x*x*x, or will he take the value of x3​​​​​​ and multiply by x? The teacher is interested in finding out this, but I don't know how to find out myself.

## Solve command Issue due to Computational Cost...

Hello Everyone;

Hope you are fine. I am solving system of odes using rk-4 method. For this purpose I formulate the "residual" (on maple file) which is further function of "x" and "y". With the help of discritization point further I convert "residual" into system of ode's. Then i used "sys111 := solve(odes_Combine, `~`[diff](var, t))" to simplify the system. Finnally i applied RK-1. Code is pasted and attached. This all process is for "N=4". When i increase the value of "N", number of Odes increase accordingly. With increasing value of "N" the comand "sys111 := solve(odes_Combine, `~`[diff](var, t))" taking a lot of time due to heavy computation. Is that any way to proceed without this comand for rk-1?

Question1.mw

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## Maxima of the given equation...

Let say,

A= A1+A2+.....................+An

B=B1+B2+.....................+Bn,

C=C1+C2+.....................+Cn

And all the values of A1 to Cn may be both positive or Negative.

Then, how to program to find the Maximum Value of  (A^2+B^2+C^2+A.B+B.C+C.A)^(1/2).

## What can block the import of data from Excel?...

I have a student who then she uses tools/assistent/import data and then the file then Maple claims the Excel file is empty? She uses Maple 2021.2. File works on other my and other student computers.

## why expanding PDE makes Maple hangs?...

To Maple support:

I was investigating this pde from a different forum.

I noticed that when using an expanded version of the pde, Maple hangs. Without expanding the PDE, Maple gives an answer in 2 seconds.

Why does expanding the PDE makes a difference? I do not have an earlier version of Maple on my new PC to check if this is a new issue or not.

 > interface(version);

 > Physics:-Version()

 > restart; pde1:=VectorCalculus:-Laplacian(u(r,theta),'polar'[r,theta]); pde1_expanded:=expand(pde1); bc  := u(1,theta)=sin(theta)^4,u(3,theta)=1; pdsolve([pde1=0,bc],u(r,theta))

 > pdsolve([pde1_expanded=0,bc],u(r,theta)); #HANGS, Waited more than 40 minutes.
 >

## Maple Matrix Question...

Let
"a"

and
"b"

be real numbers and

"A = Matrix(3, 3, [[a, a - 1, -b], [a - 1, a, -b], [b, b, 2*a -

1]])"

,
"B="

"Matrix(5, 5, [[0, a, 3, 0, a], [3, 0, 0, b, 0], [0, 1, b, 0,

1], [b, 0, 0, 1, 0], [0, a, 1, 0, b]])"

(a) Show that if
"0 <= a"

"a <= 1"

and
"b^2 = 2*a*(1 - a)"

, then A is an orthogonal matrix with determinant equal to one.
(b) For what values of a and b is the matrix B singular? Determine the inverse of B (for those values of a and b for which B is invertible).

## Find all rational function solutions to the Kadomt...

Find all rational function solutions to the Kadomtsev-Petviashvili equation

(&PartialD;)/(&PartialD;x);

diff(u, t) + 6*u*diff(u, x) + diff(u, x, x, x) - diff(u, y, y) = 0;

by u = 2
diff(ln, x, x)*f;

=(2 (((&PartialD;)^2)/(&PartialD;x^2) f) f-2 ((&PartialD;)/(&PartialD;x) f)^2)/(f^2);
with
f;
=
(a[1 ]x+a[2] y+a[3] t+a[4])^2+(a[5] x+ a[6] y+a[7] t+a[8])^2+a[9], ;
where
a[i], i=1..9, ;
are real constants.

## Problem-With-Boundary-Condition-At-Infinity...

I am having a problem in evaluating a fluid flow problem at a boundary that includes infinity using a semi-analytic method Adomian Decomposition Method.

Find the attached code. Thanks in advance.

## loop over table...

Just wondering how I do a loop over the contents of the table. I need both the index variable and the stored value associated with it.

This one apparently doesn't work.

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## How do i solve State Space system in Maple??...

Hii!!

I need your help in state space system.... kindly guide me how to solve State Space system in maplesoft.....i excecute the command but i didn't find the answer....can you plz help me?I have been trying for two weeks now but it is not working.Thank you!!

## Approximating Riemann Sums Numerically...

Hello, we need to do an integral based on two numerically approximated functions given by a second degree coupled differential equation.

The integral:
Where xs and xu are functions of the variable t.

We wish to do a half-sums to approximate the integral, that is:

Define an N = number of points, such that we get a delta_x = L/N.

We then wish to get two vectors x_s = [x_s(0),x_s(1),...,x_s(N)] and x_u = [x_u(0),x_u(1),...,x_u(N)] by running some kind of for loop over our approximation procedure.

Is there any function for this already inside of Maple? We need to approximate the integral using Riemann sums and no other method.

## "Error while printing" message when trying "Print ...

When trying to print a Maple Document as a PDF on Mac, I am now getting an "Error while printing" message. A 1-page pdf is created that's empty.   This is a new error, one that I've never seen when printing as PDF for any other Maple Document I've created.

I'm running Mac OS 12.3.1, the latest version of Mac OS and using Maple 2020.

## recursive differentiation...

I am trying to develop a recursive code to the above equations.  Note, U,X&Y are multivariate functions (in this case bivariate functions of (x,y)) i.e. U=U(x,y), X=X(x,y) etc.

## 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