Dear Users!

Hope you are doing well. Below is the code to solve system of equations

restart;M:=3;
u[0, 0] := tau[1]-2*tau[2]+3*tau[3] = 1;
u[0, 1] := tau[1]-tau[3] = 1/2;
u[0, 2] := tau[1]+2*tau[2]+3*tau[3] = 2;
SOL[0] := fsolve({seq(`$`(u[0, l1], l1 = 0 .. M-1))});

the solutions SOL[0] := {tau[1] = .7500000000, tau[2] = .2500000000, tau[3] = .2500000000}
I want to define a vector of order M*1 having the solution of of tau's like that

[.7500000000  .2500000000  .2500000000]

I'm waiting for you positive response. Thanks in advance.
Special request to:
@acer @Carl Love @Kitonum @Preben Alsholm

Hello,

I need help to approximate Fn(x,y) and Sn(y) for n>=3 to see the convergence. 

Here is the problem:

I have an integral equation Fn(x, y) defined by

F0(x,y) = 0,

F1(x,y) = (9/8)*(y+1) - (21/8)*( y*exp(-2*x) + exp(-x) )

Fn+1(x,y) = (9/8)*(y+1) - (21/8)*( y*exp(-2*x) + exp(-x) ) + (3/4)*int ( Fn( x-z, 2*y*exp(-z) ), z=0..Un(x) ), where the function Un(x) is defined below.

where I suppose that Fn(x,y) >=0 and y>=0 and x>=0. I am iterating the integral equation and find the zeros Sn(y) solutions of Fn(S(y) , y) = 0. The goal is to show that the sequence Fn(x,y) converges to some F(x,y) and Sn(y) converges to some S(y). We can also plot the curves Sn(y) to show the convergence. Notice that Sn(y) >= 0 is increasing in n and decreasing in y.

What I did :

If n = 0, I solve F1(x,y) = 0 and find analytically x = S1(y) = -ln((1/14)*(-7+sqrt(84*y^2+84*y+49))/y). Notice that F1(x,y) = 0 is quadratic in exp(-x) and then F1(x,y) = 0 is easy to solve. S1(y) is the positive function for y>=0.

If n = 1, we need to solve F2(x,y) = (9/8)*(y+1) -(21/8)*( y*exp(-2*x) + exp(-x) ) + (3/4)*int ( F1( x-z, 2*y*exp(-z) ), z, 0, U1(x) ). The function U1(x) is obtained as follows :

i) We define g( U ) = U + S1( 2*y*exp(-U) )

ii) We find the function U1(x,y) solution of g( U1(x,y) ) = x

A generalization of Un(x) is given by

i) Define g( U ) = U + Sn( 2*y*exp(-U) )

ii) Find the function Un(x,y) solution of g( Un(x,y) ) = x

The curve S2(y) :

I find the analytic function F2(x, y), but it is impossible to solve F2(x,y) = 0 and find x = S2(y) analytically. So I choose an interval [0, 10] for y and discretize that interval. Now at each point yi in [0, 10], the function F2(x, yi) depends only on x. I apply the bisection method (dichotomic method) and find the value xi such that F2(xi, yi) = 0. The data (yi, xi) gives the curve S2(y). I plot the data (yi, xi) and (y, S1(y)) in the same curve.

Question:

It is impossible to iterate the process below and find F3(x, y), F4(x,y), etc... because we cannot find U2(x), U3(x), etc... analytically. Any suggestions or helps to plot the curves (y, Sn(y)) for n = 3, 4, etc. to see the convergence ?

Thanks !

Hi

I have an ODE with 3 parameters

I'd like to make a graph that shows how its solution vary as Kac and Kd vary. This could have an axis of the form:

            | /k[d]
  B(t)  |/_ __
                t

which could contain a surface composed of the solutions as k[d] varies. Then a series of surfaces could be put together on the same axis to show what happens as kaC varies.

Some typical values are:

kaC = 6*10^(-2),
k[d1] = 7*10^(-3),
R = 1

I'd like to graph everything  in two orders of magnitude of these values for KaC and k[d1].

Currently I think the key obstacle is making a surface of solutions to the ODE; as once I can do that I think making a sequence of them on the same axis should be quite simple with Display

hello everyone,

please I need our help to find the eigenvalues (m) of this equation (eq)

thank you 

eq.mw
 

Download eq.mw

Problem copying a document to Maple Cloud (Public domain)

• Reset password

• Verified email is correct

• Chose File → Save to Cloud... (or clicked Send Document to Cloud on Maple Cloud palette) either way opend Login dialog

• Entered  Account = Maplesoft account, my Email and password then clicked Log in.  The following message appears: "The account type or email address or password is incorrect"

I've saved .mw files to Maple Cloud before with no problems.  Any help appreciated.

Thanks, Les

1,1,2,2,2,3,3,2,2,1,2,2,2,3,3,1,1

i would like to research the ordering mechanism of this kind of series Before sorting.

HI, 

Yesterday I replied  denitsastaicova's question while providing an attached file. 

Surprisingly, I wasn't able to save the worksheet after having executed it. The only way I found to save it was to copy-paste it's content in a new worksheet and save this latter without any execution.
Here is the file
events.mw

For info I'm working with  Standard Worksheet Interface, Maple 2015.2, Mac OS X, December 21 2015 Build ID 1097895
on Mac OS Mojave 10.14.3
If I open this file and execute it (and even if I execute only the commands from the initial restart to the three dsolve), I get this pop-up error message when trying to save it:

Does my worksheet contain some undesired character or is it a bug ?

Starting from 3 points of a base, then got 3 lines equations.

If having 3 lines equations of a cone surface, how to find the surface equation of a cone?

I find many tools about differential 

i had some differential ideal

how to use these tools to research what application can be applied with differential ideals I discovered?

do math regex solver exist in this world?

expect to output a set of regex for pattern

and then use regex to generate condition or rules equations and then use sorting algorithm to find whether match all data

Dear Users!

Hope you would be fine. I want to export .dat file from 2D plots in attached file. But facing some problem. Please have a look and try to fix it.

Many thanks

2._SP_alpha_varies.mw

Special request:

@Carl Love

@acer

@Kitonum

Dear Users!

Hope you would be fine. I want to export dat file for 3D plot in maple and want to replot it any perfessional software like tecplot, origin.

u:=sin(x+y):
plot3d(sin(x+y), x = 0 .. 2*Pi, y = 0 .. 2*Pi);
How can I export the data in 3D. Thanks in advance for you help.

Even for very common functions Maple has trouble calculating a series expansion if the center is not zero.

series(sin(x),x=0);

works as expected. But choosing x = 1 as center yields

series(sin(x),x=1);

This strange behavior also happens with other standard functions like cos, cosh, sinh.

So I have this expression

f:=(coth(x)^(1/3)-tanh(x)^(1/3))*(coth(x)^(2/3)+tanh(x)^(2/3)+1)

which Maple can not simplify?

I need to do it like this

`assuming`([expand(simplify(add(`~`[simplify]([op(combine(expand((coth(x)^(1/3)-tanh(x)^(1/3))*(coth(x)^(2/3)+tanh(x)^(2/3)+1))))]))))], [x > 1])

Is this actually true or what is happening here?