The ability of Maple to solve differential equations is unsurpassed, but when the solutions appear in terms of Heun functions that result is disappointing because it is either difficult or impossible to convert those functions to other functions more commonly used and for which plots are readily generated.

Specifically, does any reader have a suggestion what to do with Heun C and Heun G functions?  In principle, they seem to be related to 1F1 and 2F1 hypergeometric functions, but the conversion seems not to succeed, and it is not obvious how to make it succeed.  In both cases of interest, the literature contains hints of solutions in other functions.

It seems that a solution of a differential equation in terms of Heun functions is not a solution at all.

Today science professionals in engineering software used to only work on the desktop and even just looking to download and use mobile apps math; but they are not able to design their own applications.Maplesoft to set the solution to it through its Maple package; software supports desktop and mobile; solves problems of analysis and calculation with Embedded Components. To show this we have taken the area of different mathematical topics; fixed horizontally to a certain range of parameters and not just a constant as it is customary to develop. This paper shows how the Embedded Components allow us to develop mathematics in all areas. Achieving build applications that are interactive in mobile devices such as tablets; which are used at any time. Maple gives us design according to our university or research need, based on contemporary and modern mathematics.With this method we encourage students, teachers and researchers to use graphics algorithms.

CSMP_PUCP_2014.pdf

Coloquio_PUCP.mw

Lenin Araujo Castillo

Physics Pure

Computer Science

Download FermiCreationAnnihilation.mw

Dear all,

I have one quetion. I have written maple code based on Dr.Robert J. Lopez's one.

Here is my code.

> q1 := diff(x(t),t) = -a*x(t)*y(t) + b*z(t);

q2 := diff(y(t),t) = -a*x(t)*y(t) + b*z(t);

q3 := diff(z(t),t) =  a*x(t)*y(t) - b*z(t);

q4:=k(t)=x(t)*y(t)/z(t);

ic := x(0)=10,y(0)=10,z(0)=0;

C := < I put Experimental data….>:

> SS := proc(a,b)

local F, V;

if not type([a,b],['numeric','numeric']) then return 'SS'(a,b);

elif a<0 or b<0 then return 1e100;

end if;

F := dsolve(eval({q1,q2,q3,q4,ic},{:-a=a,:-b=b}),[x(t),y(t),z(t),k(t)],numeric, output=Array([seq(k,k=0..N)]));

V := convert(Column(F[2,1],5),Vector);

Norm(V-C,2);

end proc:

 I just put one more equation -eqn4. it is not differential equation.

I currently have error massage from maple. Could you let me know how I solve the equations in this case?

Thanks.

Hello,

Since I was working in Matlab with Galerkin method which implies periodic boundary conditions I was wondering how to implement this in maple.

I tried this:

restart;

pde2 := diff(u(x, t), t)+3*(diff(u(x, t)^2, x))+diff(u(x, t),x$3) = 0

IBC := {u(0, t) = u(2, t), u(x, 0) = sech(50*(x-1/2))^2+2*sech(30*(x-1))^2, (D[1](u))(0, t) = (D[1](u))(2, t), (D[2](u))(0, t) = (D[2](u))(2, t)}

pds := pdsolve(pde2, IBC, numeric, time = t, range = 0 .. 2)

But it's telling me: 

Error, (in pdsolve/numeric/process_IBCs) initial/boundary conditions can only contain derivatives which are normal to the boundary, got (D[2](u))(0, t)

So what's wrong?

following commands on my computer got an error.

restart;
with(LinearAlgebra):
A:=Matrix([[1,3],[2,5]],datatype=float):
b:=Vector([1,1],datatype=float):
LinearSolve(A,b,method=hybrid);
Error, (in SWcallhybrid[1]) param 4 should be an rtable

any suggestion is appreciated.

win7, 12.02

Hi,

I'm sorry, a few das ago I asked about it. Problamy my question was unclear.
I've decieded asking again.

I need a prcocedure (or contitional loops/sequences) which allow me to put values which are equivalent
to symbols into the array. The value are taken from eight diferent list. 

I enclose maple worksheet and screenshoot with explanation what I need.

I wil be appreciated for any help.

DA_-_help.mw

Dear all, I have been trying to use Runge-Kutta method to plot an approximate solution with the following code. However, although I can get the numerical approximation the plot would not show.

h := .1;

x[0] := 0;

y[0] := 1;

xf := 3;

n := floor(xf/h)

f:= (x,y)->1/(3 y-x-2)

x := x[0]

y := y[0]

for i to n do

k1 := f(x, y);

k2 := f(x+(1/2)*h, y+(1/2)*h*k1);

k3 := f(x+(1/2)*h, y+(1/2)*h*k2);

k4 := f(x+h, h*k3+y);

k := (k1+2*k2+2*k3+k4)*(1/6);

y := h*k+y;

x := x+h

end do;

y[n]

data := [seq([x[n], y[n]], n = 0 .. 30)];

p[2] := plot(data, style = point, color = blue);

p[3] := plot(data, style = line, color = blue);
display(seq(p[n], n = 2 .. 3));

Does anyone in the community know example worksheets that analyze "billiards", viz. trajectory sets of free, specularly reflected particles constrained to bounce around in a particular 2d domain?

Are there any examples using the Bunimovich Stadium Billiard?

Thanks,

Bob Terry

declare(W(x, y), Z(x, y));

sys := [-A*kappa3-`&PartialD;`(`&PartialD;`(W(x, y))/`&PartialD;`(x))*(2*G-A)/`&PartialD;`(x)-2*G*(`&PartialD;`(`&PartialD;`(W(x, y))/`&PartialD;`(y))/`&PartialD;`(y)+`&PartialD;`(`&PartialD;`(Z(x, y))/`&PartialD;`(x))/`&PartialD;`(y))+A*`&PartialD;`(`&PartialD;`(Z(x, y))/`&PartialD;`(x))/`&PartialD;`(y) = 0, `&PartialD;`(`&PartialD;`(Z(x, y))/`&PartialD;`(y))*(A-4*G)/`&PartialD;`(y)+`&PartialD;`(`&PartialD;`(W(x, y))/`&PartialD;`(x))*(A-2*G)/`&PartialD;`(y)-2*G*`&PartialD;`(`&PartialD;`(Z(x, y))/`&PartialD;`(x))/`&PartialD;`(x) = 0];

I have this system of coupled PDE and I wish to solve it using Maple.

It gives me error of this kind:

pdsolve(sys, [[W(x, y)], [Z(x, y)]]);

Error, (in pdsolve/sys) found functions depending on different variables in the given DE system: [`&PartialD;`(x), `&PartialD;`(y)]

Thanks a lot for help

I don't know what mean is T and V0x?

Please.

Dear all,

I want to know how can I solve a fourth or higher order equation to find out its roots, actually coefficients of each power terms itself are functins of other parameters not constant.

Please reply as soon as possible, as this is very urgent,

Regards.

I'd like to pay attention to the article of David Austin "How to Grow and Prune a Classification Tree"

Here is its introduction:

"

It's easy to collect data these days; making sense of it is more work. This article explains a construction in machine learning and data mining called a classification tree. Let's consider an example.

In the late 1970's, researchers at the University of California, San Diego Medical Center performed a study in which they monitored 215 patients following a heart attack. For each patient, 19 variables, such as age and blood pressure, were recorded. Patients were then grouped into two classes, depending on whether or not they survived more than 30 days following the heart attack.

Assuming the patients studied were representative of the more general population of heart attack patients, the researchers aimed to distill all this data into a simple test to identify new patients at risk of dying within 30 days of a heart attack.

By applying the algorithm described here, Breiman, Freidman, Olshen, and Stone, created a test consisting of only three questions---what is the patient's minimum systolic blood pressure within 24 hours of being admitted to the hospital, what is the patient's age, does the patient exhibit sinus tachycardia---to identify patients at risk. In spite of its simplicity, this test proved to be more accurate than any other known test. In addition, the importance of these three questions indicate that, among all 19 variables, these three factors play an important role in determining a patient's chance of surviving.

Besides medicine, these ideas are applicable to a wide range of problems, such as identifying which loan applicants are likely to default and which voters are likely to vote for a particular political party.

In what follows, we will describe the work of Breiman and his colleagues as set out in their seminal book Classification and Regression Trees. Theirs is a very rich story, and we will concentrate on only the essential ideas"

It would be interesting to compare this approach with discriminant analysis. Hope somebody of  the Maple developers will give a concrete example on this theme with Maple.

How do I use msolve to solve y^2 + y - 11=0 in Zp for all primes p with 41=< p =<107 ?

Also, using the results make a conjecture describing the primes p for which there are solutions to y^2 + y - 11 = 0 in Zp

This was what I did.

41<=p<=107

msolve(y^2 + y - 11=0, p)

but I received this error, no implementation of msolve matches the arguments in call, msolve(y^2 + y - 11=0, p)

Any help is appreciated. Thanks

I have a coefficient matrix A and the constant matrix b.

I want to find the unknowns x_1,x_2,...,x_8. When I put my code and run it in Maple I get an error. Any ideas as to why this is happening? The code I tried is as follows:

with(Student[NumericalAnalysis]):

A := Matrix([[-1, 0, 0, (1/2)*sqrt(2), 1, 0, 0, 0], [0, -1, 0, (1/2)*sqrt(2), 0, 0, 0, 0], [0, 0, -1, 0, 0, 0, 1/2, 0], [0, 0, 0, -(1/2)*sqrt(2), 0, -1, -1/2, 0], [0, 0, 0, 0, -1, 0, 0, 1], [0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, -(1/2)*sqrt(2), 0, 0, (1/2)*sqrt(3), 0], [0, 0, 0, 0, 0, 0, -(1/2)*sqrt(3), -1]]);

b := Vector([0, 0, 0, 0, 0, 10000, 0, 0]);

LinearSolve(A, b, maxiterations = 300, method = SOR(1.25), tolerance = 10^(-2));

I also tried it with a SOR variable of 1.5 instead of 1.25, but that gives me the same error.