Maple Questions and Posts

Solving a nonlinear hyperbolic PDE...

Asked by: Al86 150

September 04 2015

1 0

I am considering the following PDE and I am getting an error, please suggest a better numerical method than the default one used in maple:

the PDE is:

u_{xx}u^3 - sin(xt)u_{tt} = u(x,t)

u(x, 0) = sin(x), (D[2](u))(x, 0) = cos(x), u(0, t) = cos(t), (D[1](u))(0, t) = sin(t)

Please suggest me a method that will also work for the following PDEs:

u^m* u_{xx} - sin(xt)u_{tt} = u^n

for m,n =0,1,2,3,... for the cases m=n and m not equal n

Here's the code:

>

(1)

>

(2)

>

pds := pdsolve(pde, [ibc], numeric, time = t, range = 0 .. 1, spacestep = 0.1e-1)

(3)

>

pds:-plot3d(u(x, t), t = 0 .. 1, x = 0 .. 1, labels = [t, x, u(x, t)], labelfont = [times, bold, 20], axesfont = [times, bold, 16])

Error, (in pdsolve/numeric/plot3d) unable to compute solution for t>HFloat(0.0):
Newton iteration is not converging

>

Download nonlinear_hyperbolic_PDE.mw

How do i save a compiled worksheet on Mac OSX?...

Asked by: Winkel 5

September 04 2015

1 5

Hi,

I'm trying to compile a worksheet and save it on Mac OSX. The worksheet ends with this code:

>

> save `E:\\class work\\THERMODYNAMICS\\ThermoSoft\\Compiled\\SteamTables.m`;

>

The guide tells me to change the path to a user specified folder where the .m file will be saved.

Since the path name already given is a Windows path, I have to change that to a Mac path.

My problem is, that i don't know what I should write?

I have tried writing:

save `\\Macintosh HD\\Users\\Name\\Folder\\SteamTables.m`;

But it gives an error, and can't save the file.

Portfolio Optimization

by: MrMarc 3163 Product: Maple

September 04 2015

2 0

LL_104)_NASDAQ.mw
Portfolio_Optimization.txt

Portfolio Optimization with Google Spreadsheet and Maple

I will in this post show how to manage data and do portfolio optimization in Maple by using google spreadsheet.

You can either use a direct link to the data:

https://docs.google.com/spreadsheets/d/1L5-yUB0EWeBdJNMdELKBRmBQ1JJ0QymrtDLkVhHCVn8/pub?gid=649021574&single=true&output=csv

or you can set up your own google spreadsheet. If you choice to set up your own spreedsheet follow the below road map:

1) select which market you want to follow:

NASDAQ

http://www.nasdaq.com/screening/companies-by-industry.aspx?exchange=NASDAQ&render=download

NYSE

http://www.nasdaq.com/screening/companies-by-industry.aspx?exchange=NYSE&render=download

AMEX

http://www.nasdaq.com/screening/companies-by-industry.aspx?exchange=AMEX&render=download

2) Create a new google spreadsheet and name two sheets Blad1 and Panel. In the first cell of Blad1 you put the formula:

=IMPORTDATA("http://www.nasdaq.com/screening/companies-by-industry.aspx?exchange=NASDAQ&render=download")

you need to change the url to match your selection in 1).

3) In the first cell of Panel you put the name "Ticker" and then you copy all the ticker names from Blad1.

4) In the script editor you put in the below java script code:

function PanelCreation_Stock()

{
var ss = SpreadsheetApp.getActiveSpreadsheet();
var sourceSheet = ss.getSheetByName("Blad1");
var dstSheet = ss.getSheetByName("Panel");
var curDat = new Date();
var day1 = curDat.getDay();
if(day1 == 0 || day1 == 1)
{
return;
}
var lCol = dstSheet.getLastColumn();
var srcdate = dstSheet.getRange(1, 1, 1, lCol).getValues();

for(var k=1;k<=srcdate[0].length-1;k++)
{
if(Utilities.formatDate(srcdate[0][k],"GMT", "dd-MMM-yy") == Utilities.formatDate(curDat,"GMT", "dd-MMM-yy"))
{
return;
}
}
var snRows = sourceSheet.getLastRow();
var dnRows = dstSheet.getLastRow();

var srcStock = sourceSheet.getRange("A2:A" + snRows).getValues();
var srcLastSale = sourceSheet.getRange("C2:C" + snRows).getValues();

var dstStock = dstSheet.getRange("A2:A" + dnRows).getValues();
var dstLastSale = dstSheet.getRange("Z2:Z" + dnRows).getValues();

for(var j=0;j<dnRows-1;j++)
{
dstLastSale[j][0]="n/a";
}
var flag = "true";
var foundStock;
for(var i=0;i<snRows-1;i++) //snRows
{
var sStockVal = srcStock[i][0];

//var foundStock = ArrayLib.indexOf(dstStock,0, sStockVal);

flag="false";
for(var j=0;j<dnRows-1;j++)
{
if(dstStock[j][0].toString().toUpperCase() == srcStock[i][0].toString().toUpperCase())
{
flag = "true";
foundStock = j;
break;
}
}
if(flag=="true")
{
dstLastSale[foundStock][0] = srcLastSale[i][0];
}
else
{
var dnRows1 = dstSheet.getLastRow()+1;
dstSheet.getRange("A" + dnRows1).setValue(srcStock[i][0]);
dstSheet.getRange(dnRows1,lCol+1,1,1).setValue(srcLastSale[i][0]);
for(var k=2;k<=lCol;k++)
{
if(dstSheet.getRange(dnRows1, k).getValue()=="")
{
dstSheet.getRange(dnRows1, k).setValue("n/a");
}
}
}
}
dstSheet.getRange(1,lCol+1).setValue(curDat);
dstSheet.getRange(2, lCol+1, dstLastSale.length, 1).setValues(dstLastSale);
}

5) Set it to run each day at 12:00. The code will save the new last sale price for monday to friday with one days lag.

Now we can move on to Maple.

In Maple run the following code to load the data:

X := proc (Url) local theDLL, URLDownloadToFile, myDirectory, myFile, Destination, DL;

theDLL := "C:\\WINDOWS\\SYSTEM32\\urlmon.dll";

URLDownloadToFile := define_external('URLDownloadToFileA', pCaller::(integer[4]), szURL::string, szFileName::string, dwReserved::(integer[4]), lpfnCB::(integer[4]), 'RETURN'::(integer[4]), LIB = theDLL);

if FileTools[Exists]("C:\\mydir") = true then FileTools:-RemoveDirectory("C:\\mydir", recurse = true, forceremove = true) else end if;

FileTools:-MakeDirectory("C:\\mydir");
myDirectory := "C:\\mydir";
myFile := "data1.csv";
Destination := cat(myDirectory, "\\", myFile);

DL := proc () local M;

URLDownloadToFile(0, Url, Destination, 0, 0);
M := ImportMatrix("C:\\mydir\\data1.csv", delimiter = ",", datatype = string);
M := Matrix(M, datatype = anything)

end proc;

return DL()

end proc:

data := X("https://docs.google.com/spreadsheets/d/1L5-yUB0EWeBdJNMdELKBRmBQ1JJ0QymrtDLkVhHCVn8/pub?gid=649021574&single=true&output=csv");
L := LinearAlgebra:-Transpose(data);

If you use your own spreadsheet you need to change the url to match that spreadsheet.
Select File -> Publish to the web in google spreadsheet

We can now run the portfolio optimization in Maple:

with(Statistics):
with(ListTools):
with(LinearAlgebra):
with(Optimization):
with(plots):

Nr, Nc := ArrayTools:-Size(L):
symb := L[1 .. 1, 2 .. Nc]:
LL := L[2 .. Nr, 2 .. Nc]:
Nr, Nc := ArrayTools:-Size(LL):

# Removing stocks with missing observations
for i to Nc do if Occurrences("n/a", convert(Column(LL, i), list)) >= 1 then AA[i] := i else AA[i] := 0 end if
end do;

DD := RemoveInRange([seq(AA[i], i = 1 .. Nc)], 0 .. 1):
symbb := DeleteColumn(symb, DD):
LLL := map(parse, DeleteColumn(LL, DD)):
Nr, Nc := ArrayTools:-Size(LLL):

# Calculate Return
for j to Nc do
for i from 2 to Nr do

r[i, j] := (LLL[i, j]-LLL[i-1, j])/LLL[i-1, j]

end do
end do;

RR := Matrix([seq([seq(r[i, j], j = 1 .. Nc)], i = 2 .. Nr)], datatype = float[8]);
n, nstock := ArrayTools:-Size(RR):

# Portfolio Optimization
W := Vector(nstock, symbol = w):
y := Vector(n, fill = 2, datatype = float[8]):
s1 := Optimization[LSSolve]([y, RR])[2];
Nr, Nc := ArrayTools:-Size(s1):

j := 0:
for i to Nr do if s1[i] <> 0 then j := j+1; ss1[j] := symbb[1, i] = s1[i] end if end do;

Vector(j, proc (i) options operator, arrow; ss1[i] end proc);
LineChart(s1);

Error in DEplot...

Asked by: LeeHoYeung 535

September 03 2015

0 7

eq1 := a(t)*(diff(a(t), t))+a(t)*(diff(a(t), t))*b(t)*(diff(b(t), t))*c(t)*(diff(c(t), t));
eq2 := a(t)*(diff(a(t), t))+a(t)*(diff(a(t), t))*c(t)*(diff(c(t), t))+a(t)*(diff(a(t), t))*b(t)*(diff(b(t), t))*c(t)*(diff(c(t), t));

DEplot({eq1, eq2}, [b(t), c(t)], t = 0 .. 1, b = 0 .. 1, c = 0 .. 1, [[b(0) = 1, c(0) = 1]], arrows = large);

Error, (in DEtools/DEplot/CheckDE) only derivatives of dependent variables can be present

DEplot({eq1 = 3*t^2, eq2 = 2*t^3}, [b(t), c(t)], t = 0 .. 1, b = 0 .. 1, c = 0 .. 1, [[b(0) = 1, c(0) = 1]], arrows = large);
Error, (in DEtools/DEplot/CheckDE) only derivatives of dependent variables can be present

Error message in this code...

Asked by: kippendorf 5

September 03 2015

1 19

HI there,

I m getting an error message . Could someone help me

v1 := int(cos(tau)*g(tau), tau = t0 .. t);
int(cos(tau) g(tau), tau = t0 .. t)
v2 := int(-sin(tau)*g(tau), tau = t0 .. t);
int(-sin(tau) g(tau), tau = t0 .. t)
soln := C1*y1+C2*y2+v1*y1+v2*y2;
C1 y1 + C2 y2 + (int(cos(tau) g(tau), tau = t0 .. t)) y1

+ (int(-sin(tau) g(tau), tau = t0 .. t)) y2
soln := combine(soln);
(int(-y2 sin(tau) g(tau) + y1 cos(tau) g(tau), tau = t0 .. t))

+ C1 y1 + C2 y2
eval(soln, t = t0) = 0, eval(diff(soln, t), t = t0);
C1 y1 + C2 y2 = 0, -y2 sin(t0) g(t0) + y1 cos(t0) g(t0)
solve({%}, {C1, C2});
soln := eval(soln, %);
Error, invalid input: eval received (C1*y1+C2*y2 = 0, -y2*sin(t0)*g(t0)+y1*cos(t0)*g(t0)), which is not valid for its 2nd argument, eqns

Zooming-in with no axes, again......

Asked by: Yiannis Galidakis 150

September 03 2015

2 9

Hi everyone,

Consider this Maple 18 doc:

FareySeq.mw

I am having the same problem as in:

http://www.mapleprimes.com/questions/203593-Maple-13-Fast-Maple-18-Crawling#comment213548

Namely, the produced animated .gif contains only one frame. Animation doesn't work, even though the button of the animation is active after I click on frame #1.

I have acer's solution at the end, but it doesn't work in this case either.

Breaks in both Maple 13 and 18.

TIA,

Yiannis

Distance of point to plane...

Asked by: pathfinder73 15

September 03 2015

2 19

Hello!

With Maple 2015, license Student, is it possible calculate distance between point and plane in R³ ? Package geom3d is recommended for this or another? How can I calculate this?

Thank you so much!

Passing a vector element to solve function...

Asked by: abbeykabir 85

September 03 2015

0 1

adomian decomposition method...

Asked by: wafa 10

September 03 2015

0 1

Hello

anyone plz help me to find adomian decomposition method (ADM) maple code, also how to find the adomian polynomials separately using maple, i search it for a long time but did'nt succeeded,

PDEs and Boundary Conditions - new developments

by: ecterrab 14570 Product: Maple

September 03 2015

8 1

The PDE & BC project , a very nice and challenging one, also one where Maple is pioneer in all computer algebra systems, has restarted, including now also the collaboration of Katherina von Bülow.

Recapping, the PDE & BC project started 5 years ago implementing some of the basic methods found in textbooks to match arbitrary functions and constants to given PDE boundary conditions of different kinds. At this point we aim to fill gaps, and the first one we tackled is the case of 1st order PDE that can be solved without boundary conditions in terms of an arbitrary function, and where a single boundary condition (BC) is given for the PDE unknown function, and this BC does not depend on the independent variables of the problem. It looks simple ... It can be rather tricky though. The method we implemented is a simple however ingenious use of differential invariants to match the boundary condition.

The resulting new code, the portion already tested, is available for download in the Maplesoft R&D webpage for Differential Equations and Mathematical Functions (the development itself is bundled within the library that contains the new developments for the Physics package, in turn within the zip linked in the webpage).

The examples that can now be handled, although restricted in generality to "only one 1st order linear or nonlinear PDE and only one boundary condition for the unknown function itself", illustrate well how powerful it can be to use more advanced methods to tackle these tricky situations where we need to match an arbitrary function to a boundary condition.

To illustrate the idea, consider first a linear example, among the simplest one could imagine:

>

(1)

>

(2)

Input now a boundary condition (bc) for the unknown such that this bc does not depend on the independent variables ; this bc can however depend on arbitrary symbolic parameters, for instance

>

(3)

With the recent development, this kind of problem can now be solved in one go:

>

(4)

Nice! And how do you verify this result for correctness? With pdetest , which actually also tests the solution against the boundary conditions:

>

(5)

And what has been done to obtain the solution (4)? First the PDE was solved regardless of the boundary condition, so in general, obtaining:

>

(6)

In a second step, the arbitrary function got determined such that the boundary condition is matched. Concretely, the mapping _F1 is what got determined. You can see this mapping reversing the solving process in two steps. Start taking the difference between the general solution (6) and the solution (4) that matches the boundary condition

>

(7)

and isolate here

>

(8)

So this is the value that got determined. To see now the actual solving mapping _F1, that takes for arguments and and returns the right-hand side of (8), one can perform a change of variables introducing the two parameters and of the _F1 mapping:

>	${tau__1 = -x+y, tau__2 = -x+z, tau__3 = z}$

${tau__1 = -x+y, tau__2 = -x+z, tau__3 = z}$

(9)

>	$solve({tau__1 = -x+y, tau__2 = -x+z, tau__3 = z}, {x, y, z})$

${x = -tau__2+tau__3, y = -tau__2+tau__1+tau__3, z = tau__3}$

(10)

>	$PDEtools:-dchange({x = -tau__2+tau__3, y = -tau__2+tau__1+tau__3, z = tau__3}, _F1(-x+y, -x+z) = (1/4)exp(-x+z-1)(x^2-2xz-y^2+2yz+2x-2y), proc (u) options operator, arrow; simplify(u, size) end proc)$

_F1(tau__1, tau__2) = -(1/4)*exp(tau__2-1)*tau__1*(tau__1-2*tau__2+2)

(11)

So the solving mapping _F1 is

>

_F1 = (proc (tau__1, tau__2) options operator, arrow; -(1/4)*exp(tau__2-1)*tau__1*(tau__1-2*tau__2+2) end proc)

(12)

Wow! Although this pde & bc problem really look very simple, this solution (12) is highly non-obvious, as is the way to get it just from the boundary condition and the solution (6) too. Let's first verify that this mapping is correct (even when we know, by construction, that it is correct). For that, apply (12) to the arguments of the arbitrary function and we should obtain (8)

>

(13)

Indeed this is equal to (8)

>

(14)

Skipping the technical details, the key observation to compute a solving mapping is that, given a 1st order PDE where the unknown depends on independent variables, if the boundary condition depends on arbitrary symbolic parameters , one can always seek a "relationship between these parameters and the differential invariants that enter as arguments in the arbitrary function _F1 of the solution", and get the form of the mapping _F1 from this relationship and the bc. The method works in general. Change for instance the bc (3) making its right-hand side be a sum instead of a product

>

(15)

>

(16)

>

(17)

An interesting case happens when the boundary condition depends on less than parameters, for instance:

>

(18)

>

f(x, y, z) = ((x-z+1)*_C1+x-y)*exp(((z-1)*_C1+y)/(1+_C1))/(1+_C1)

(19)

As we see in this result, the additional difficulty represented by having few parameters got tackled by introducing an arbitrary constant _C1 (this is likely to evolve into something more general...)

>

(20)

Finally, consider a nonlinear example

>

(21)

>

(22)

Here we have 2 independent variables, so for illustration purposes use a boundary condition that depends on only one arbitrary parameter

>

(23)

All looks OK, but we still have another problem: check the arbitrary function _F1 entering the general solution of pde when tackled without any boundary condition:

>

(24)

Remove this RootOf to see the underlying algebraic expression

>

(25)

So this is a pde where the general solution is implicit, actually depending on an arbitrary function of the unknown The code handles this problem in the same way, just that in cases like this there may be more than one solution. For this very particular bc (23) there are actually three solutions:

>

(26)

Verify these three solutions against the pde and the boundary condition

>

(27)

:)

Download PDEs_and_Boundary_Conditions.mw

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

Programming and differentiation...

Asked by: Dmitry Lyakhov 115

September 02 2015

3 2

I have an expression of derrivative, lets say (D[2, 2](G))(x, y).

How to get this numbers - [2,2] programmicaly from it?

Make a graph for sinus...

Asked by: renethch 5

September 02 2015

1 1

hi maple is new to me.

i am trying to make a sinus graph f(x)=0,84*sin(0,017*x-1,3)+12,13

But its not possible to get the graph,

anywhere i can see how to do this so the graph is made?.

Can't find a recent post I made - mapleprimes sear...

Asked by: Christopher2222 6035

September 02 2015

0 0

I made reference to the show the enemy below and included part of the script an interesting part in the show.

I did a mapleprimes search - only two returns none of which were what I was looking for. I also did a google search which turned up nothing.

Was my post deleted?

How to hide the expression leaving the label...

Asked by: EugeneKalentev 85

September 02 2015

1 3

Hello. Using a symbol ":", you can hide the derivation of the expression. However, it lost the label of expression. Can I hide the expression of retaining the label for further use? It would be handy when working with large expressions.

What is wrong with my code...

Asked by: emmantop 40

September 01 2015

1 4

Hello,

the attached code return error for this values [0, 0.2, 0.4, 0.6] but work perfectly for this [0.2, 0.4, 0.6, 0.8]. I want it to start from 0 value. How do i correct the error? See the worksheet here com.mw

Thanks.

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