I've got a function f(x_n) = (x_n-1)^3

and need to show that for the iterative method

x_(n+1)= x_n - f(x_n)/(sqrt(f'(x_n)^2-f(x_n)*f''(x_n), at a simple root we have cubic convergence while at a multiple root, it converges linearly.

I understand that the approach is to write either a recursive function or a sequence, but i'm confused about the structure since both x and n are being incremented

I need to show what happens to the zero r=20 of f(x)= (x-1)(x-2)..(x-20)-(1/10^8)*(x^19) and the hint given is that the secant method in double precision gives an approximate in [20,21].

At present, I'm calling the secant method on f with a tolerance of 1/(10^12) with an initial x=20, but I'm stuck as to what the second initial value would be. What is the right approach to this question?

I've plotted the graph for this max function. Is there any way I can find the points of discontinuity in general and then use that to compute the derivatives at points where it exists?

I'm trying to get the RHL of exp1:=(2/(1+e^(-1/x)) as x->0+

and have l2:=limit(exp1,x=0,right) but that isn't giving me a value. How do I correct this? 

I have several plots and I'm using the display procedure,

display(seq(p1[i], i = 1..3), pts1, pts2);

to draw them. I want them to be displayed in the specified order, i.e., pts1 and pts2 should be in the foreground. Unfortunately, the display procedure ignores the order. How to enforce the specified order?

I am facing a kind of strange problem. Whenever I enter Int(exp(-s t) t^2,t) and try to see full solution using Student[Calculus1]:-ShowSolution(), it gives empty square brackets [ ] as superscripts of e. If I restart Maple engine and perform the same, sometimes it produces right solution. Kindly help, what is this? Same integral does not give problem if done with parameter 'r' instead of 's'.

At the internet site of The Heun Project, a strong declaration is made that only Maple incorporates Heun functions, which arise in the solution of differential equations that are extremely important in physics, such as the solution of Schroedinger's equation for the hydrogen atom.  Indeed solutions appear in Heun functions, which are highly obscure and complicated to use because of their five or six arguments, but when one tries to convert them to another function, nothing seems to work.  For instance, if one inquires of FunctionAdvisor(display, HeunG), the resulting list contains

"The location of the "branch cuts" for HeunG are [sic, is] unknown ..." followed by several other "unknown" and an "unable". Such a solution of a differential equation is hollow.

Incidentally, Maple's treatment of integral equations is very weak -- only linear equations with simple solutions, although procedures by David Stoutemyer from 40 years ago are available to enhance this capability.

When can we expect these aspects of Maple to work properly, for applications in physics?

hi, is there a way to collect all commands in one place which have been used during a clickable math session of a document? in fact this would help in creating automated tasks.

I paste below a simple code illustrating what I want to create: two lists from a set with pairs. I wonder it is a very simple task but I my lists aren't create in the end. 

> restart;
>
> lista:=[[1,10],[2,20],[3,30]]:
> x:=[]:
> y:=[]:
>
> for i from 1 to nops(lista) do
>     for j from 1 to 2 do
>
>         if j = 1 then
>             x[i,j]:=op(1,op(i,lista));
>        fi;
>        if j = 2 then
>             y[i,j]:=op(2,op(i,lista));
>       fi;
>    od;
> od;
>
> x;
> y;

In resume then after the for loop is terminated I want to be left with two lists:

x:= [1,2,3] and y:=[10,20,30]. I'm sure it has a quick fix but I'm stuck and would appreciate any help/advice.  

Thanks in advance!

Dear Maple users

I have a question which is maybe easily solved, but I cannot seem to find the solution myself. A vector X of coefficients has been computed earlier in the Maple document and I want these coefficients placed in front of some written symbols in order to make Maple display the final result in a nice way. I made an attempt with the Vector command as shown in the image, but I cannot make the indices start at -2. In addition I want some written math placed in front of the expression. In fact I want it displayed like shown on the image marked with a red rectangle. I did write this manually, but want Maple to do it automatically when given the coefficients vector calculated earlier. I hope someone can help me here!

(It is about finite difference methods, by the way)

Regards,

Erik 

How to numerically solve the problem

with Maple? Such type problems arise in elasticity theory (for example, see https://zbmath.org/?q=an:01366371).

Edit. Typo in the code:sin(y(x)) instead of sin(x).

How I can get a list of all label refernces of a worksheet. In fact I want to write a small code which would produce the LaTex output (written to a text file) for my indicated labels. thanx

I've got the following double integral over a region A:

e^(1/x*y)/(y^2)*(x+1)^2 where A={(x,y):1/2<=x*y<=2,1<=x<=3}

to evaluate this:

I've tried :

int6:=int(int(e^(1/x*y)/((y^2)*(x+1)^2),x=1..3),y=(1/2)..(2/3));

since the largest lower bound and smallest upper bound for y based on 1/2<=xy<=2 are 1/2 and 2/3 respectively.

This statement however, only evaluates the inner integral; is my approach correct?

I've got a function y(x) that is initially defined as x^3+y^3=1 and need to plot it, and find y',y''.

At present, I've used implicitplot(x^3+y^3=1,x=0..5,y=0..5) to plot it, but that doesnt seem to work. Also, to find y'

I've used the statement

implicitdiff(g(x,y),y(x),x) where g:=(x,y)->x^3+y^3=1 but this gives me an error that my input is invalid; y(x) is expected to be of the form {(name, set(name), set(function(name))}.

I don't quite understand..

I would like to know how to verify
y=x e5x cos(2x)
is a solution to the differential equation
y(4) -20 y”’+158 y”-580y’+841y=0