## Issue in rk-4 and Runge-Kutta-Fehlberg method...

Hello Everyone;

Hope you are fine. I am applying rk-4 and Runge-Kutta-Fehlberg method for system of odes but there is no difference in the result of these method. Can anybody guide about that for my problem. I have uploaded the code. Thanks in advance.

Question#3.mw

## Solve system of equations in Maple...

Hello!

How do I solve this system? could someone help me please.

restart;
eqns := {x(t+1) = (1+10^(-6)*(0.4e-2-0.6e-2)/(0.1e-3))*x(t)+0.7e-1*10^(-6)*y(t),

y(t+1) = 0.6e-2*10^(-6)*x(t)/(0.1e-3)+(1-0.7e-1*10^(-6))*y(t)};

with:
x(0) = 1
y(0) =
y(0) = 857.1428571

 (1)

 (2)

 (3)

## How can I estimate the minimum distance travelled ...

Good day all.

My particular question concerns a Traveling Salesman-type problem.

Suppose I wish to move along the x-y plane and visit specific nodes (see the attached worksheet).

Starting at the origin, A, I intend to visit four locations, B to E, and finally return to the origin point. These nodes may be visited in any order - but, my total distance travelled must be a minimum.
However, my direction of travel is restricted; namely:

1. Movement is limited to the x and y-directions only (up and down as well as left and right)
2. Horizontal (left or right) movement is permitten only at y=1 and y=10

This second rule restricts me from turning left or right in between y= 1 and 10.
The Traveling Salesman routine (attached) is constructed to select a tour that is confined to orthogonal movement but it does not observe the second restriction (i.e. move left or right when you reach y=1 or y=10).

Is there any way in which I can build this condition into the routine so that the movement along the circuit observes the restrictions?

If so - is it possible to graphically illustrate the order of travel (using arrows from point-to-point) on a point plot?

I appreciate you taking the time to read this.

MaplePrimes_May_6.mw

## does not fully plot f(x)=x^(1/3)...

I tried to graph the function f(x)=x^(1/3) but it only gives me a graph for non-negative x's, when the function f has all real numbers as its domain.

Maybe I'm doing it wrong.

Thank you.

## principle of plot points ...

ac-dc-dc1.msim

When i click off the "Plot events", the figure of Probe2 is pretty different comparing with "Plot events" is turned on. Here is my assumption: the simulation duration is 500 seconds and the plot points are 2000. Considering the frequency of sine current is 40HZ, many points cannot be ploted in the figure. So it is not a big deal for curve like Probe1 and Probe5 because  they tend to be a constant and Probe2 just reflect the tendency.

## Horizontally shifting...

Hey I’m trying to shift a function horizontally to the right.

I have the following 3 functions:

V1 := -x

V2:= -2*x + 4.95

V3:= -x + 1.665

Function V2 I want to shift l_1 to the right, and V3 I want to shift l_1 + l_2 to the right.

I know I can do this manually by define the functions:

V2:= -2*(x-l_1) + 4.95

V3:= -(x-l_1-l_2) + 1.665

Where l_1:=1.665 and l_2:=4.95

Is there a way to do this without typing it manually?

By the way it’s only for plotting, so it’s not necessary for me to actually define them, if there is a way to do it within a plot some how.

## Solution of simultaneous non linear equation....

I am trying to solve these equation using fsolve, but it returns the same valve. Please provide a solution.\

## Partial Differentiation Not Working with Units...

Hi, with Units[Simple] package loaded, I tried to differentiate a few functions using D[n] but it does not work. problem.mw

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 (2)

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 (5)

## How do i add elements from subsets?...

Hi! I've got a set of subsets S with Abeing the i-subset. I need to sum up all the x's in all the Ai's. How can this be achieved?

(ex):

sum( { {a, b, c}, {a, b, d} } )= 2a+2b+c+d

## Define antiderivatives...

Hey I’m trying to define the antiderivative for a function:

g(x) = 1

G(x) = int(g(x),x)

When I then type:

G(x) and press enter Maple gives me G(x) = x which of course is correct

But I can’t type:

G(5)

Then it gives me the error message:

Error, (in int) integration range or variable must be specified in the second argument, got 5

How to fix this?

I know I can type G(x) = x manually but I’m not interested in doing so, because in my document I’m going to have a lot of antiderivatives.

## 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.

## Taylor expansion...

I would like to perform the following expansion up to an arbitrary order. The dots refer to higher-order terms. All the coefficients are symmetric except for the first one.

Thank you very much!

## 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.
 >

## DirectSearch finds nonexisting roots...

DirectSearch finds nonexisting roots....     DirectSearch_finds_nonexisting_roots.mw

 >
 > restart
 > plot([cos(x), 0.001*x*x],x=-40..40,y=0..2)     ### test function plot
 > eq:= cos(x)= 0.001*x*x;     ###   float
 (1)
 > use RealDomain in solve(eq,x,explicit) end use   ## lacking some of the roots
 (2)
 > use RealDomain in solve(eq,x) end use
 (3)
 > fsolve(eq,x=-30)
 (4)
 > plot([cos(x), 0.001*x*x],x=-32..-31,y=0.9..1)
 > fsolve(eq,x=-32..-30);  fsolve(eq,x=-31.7..-31.4)
 (5)
 > with(DirectSearch)
 (6)
 > eq; SolveEquations(eq,AllSolutions):
 (7)
 > interface(rtablesize=90); SolveEquations(eq, AllSolutions)
 (8)

DirectSearch finds nonexisting roots!!!

Dr. Ali GÜZEL

 >