Uxx + Uyy =0

      y is less than Pi,x is greater than 0

B.c are u(0,y)=0 , u(Pi,y)=sinh*Pi*cosy

              u(x,0)=sinx , u(x,Pi)=-sinhx

How can I compute MatrixInverse, MatrixMultiply and eigenvalues(eigenvectors) faster? are there any procedures or commands that can be used instead of those three command mentioned before to speed up calculations?

1.mw

In the above document, digits must be 30.

I want to know how to program a metric g_[ ]  so that entries are zero apart from the diagonal.
Basically I am using the physics package and can set it as arbitrary or can set it to be specific values but I just want arbitrary values across the diagonal. e.g
 

with(Physics);
Setup(mathematicalnotation = true);
                 [mathematicalnotation = true]

Setup(metric = arbitrary);
 [metric = {(1, 1) = _F1(X), (1, 2) = _F2(X), (1, 3) = _F3(X), (1, 4) = _F4(X), (2, 2) = _F5(X), (2, 3) = _F6(X),  (2, 4) = _F7(X),

(3, 3) = _F8(X), (3, 4) = _F9(X),  (4, 4) = _F10(X)}]

SO here I want to keep F1 F5 F8 and F10, thanks in advance!

THIS IS WHAT I TRIED:

 

with(Physics);
Setup(mathematicalnotation = true);
Setup(Coordinatesystem = (X = [x1, x2, x3, x4]), metric = f(dx1^2+dx2^2+dx3^2+dx4^2));
    * Partial match of  'Coordinatesystem' against keyword 

       'coordinatesystems'

  Default differentiation variables for d_, D_ and dAlembertian 

   are: (Xequals(x1,x2,x3,x4))
  Systems of spacetime Coordinates are: (Xequals(x1,x2,x3,x4))
Error, (in Physics:-Setup) expected definition of a metric as a tensorial algebraic expression with two free indices; received one with free indices {}

I have a solution to a linear ODE which is very long and complicated.  The solition clearly has some parts which are repeated and so it would would be easiest to express those repeated parts as something simpler.

For example, suppose I had

x = (-b + sqrt(b^2 - 4*a*c) ) /2*a

What is the command to take x and do someting like

Z = sqrt(b^2 - 4*a*c)

x = (-b + Z)/2*a

when plotting a polar function in terms of r and theta, is there a way to animate it?  

For instance I want to animate u(r,theta)=rcos(theta) for theta between 0 and 2Pi.

i have to list 
a := sort([.17, .23, .33, .39, .39, .40, .45, .52, .56, .59, .64, .66, .70, .76, .77, .78, .95, .97, 1.02, 1.12, 1.19, 1.24, 1.59, 1.74, 2.92])

b:=[5,seq(0,i=1..19)]:

i want to make aloop on a  by saying that for i=1 eliminate b[1] from a then sort the remining elements of a 

then for i=2 eliminate b[2] from a then sort the rest elimant of a and so on  

Q1: In place of three statments like >a:=3: b:=4; c:=5, I have found from an example in this forum that one can use >(a,b,c):=(3,4,5). And I find this useful in some applications. Anyone know what version of Maple introduced this? I can find not referneces in the Maple books I have

Q2: Maple someimes gives 'naked' decimals when I use Numeric formatting. Any way of avoiding this. I would  like 0.25 not .25

Many thanks

`~`[int](convert(convert(series(x^x, x), polynom), list), x = 0 .. 1)

Can this sequence (produced above in list form) be displayed as 1, -1/2^2, 1/3^3, -1/4^4, 1/5^5 -1/6^6 etc.

That is with the powers unevaluated.

Hello,

What are the methods for writing code to the recursive matrix A  as follows?

Thanks.

When i am running a code in maple worksheet , one error is shown by maple. My code and error (in bold) is below

Instructional workheet for the FracSym package
G. F. Jefferson and J. Carminati

Read in accompanying packages: ASP, DESOLVII and initialise using the with command:

read `ASP v4.6.3.txt`:

DESOLVII_V5R5 (March 2011)(c), by Dr. K. T. Vu, Dr. J. Carminati and Miss G. 

   Jefferson

 The authors kindly request that this software be referenced, if it is used 

    in work eventuating in a publication, by citing the article:
  K.T. Vu, G.F. Jefferson, J. Carminati, Finding generalised symmetries of 

     differential equations
using the MAPLE package DESOLVII,Comput. Phys. Commun. 183 (2012) 1044-1054.

                                -------------
       ASP (November 2011), by Miss G. Jefferson and Dr. J. Carminati

 The authors kindly request that this software be referenced, if it is used 

    in work eventuating in a publication, by citing the article:
    G.F. Jefferson, J. Carminati, ASP: Automated Symbolic Computation of 

       Approximate Symmetries
    of Differential Equations, Comput. Phys. Comm. 184 (2013) 1045-1063.

with(ASP);
              [ApproximateSymmetry, applygenerator, commutator]
with(desolv);
[classify, comtab, defeqn, deteq_split, extgenerator, gendef, genvec, 

  icde_cons, liesolve, mod_eq, originalVar, pdesolv, reduceVar, reduceVargen, 

  symmetry, varchange]

Read in FracSym and initialise using the with command:
read `FracSym.v1.16.txt`;
       FracSym (April 2013), by Miss G. Jefferson and Dr. J. Carminati

 The authors kindly request that this software be referenced, if it is used 

    in work eventuating in a publication, by citing:
G.F. Jefferson, J. Carminati, FracSym: Automated symbolic computation of Lie 

   symmetries
of fractional differential equations, Comput. Phys. Comm. Submitted May 2013.

with(FracSym);
 [Rfracdiff, TotalD, applyFracgen, evalTotalD, expandsum, fracDet, fracGen, 

   split]

BASIC OPERATORS

The Riemann-Liouville fractional derivatives is expressed in "inert" form using the FracSym routine Rfracdiff.
The explicit formula for the form of these fractional derivatives may be found in I. Podlubny, Fractional differential equations: An introduction to fractional derivatives, fractional differential equations, some methods of their solution and some of their applications, San Diego, 1999.)

Rfracdiff(u(x, t),t,alpha);
                                alpha          
                             D[t     ](u(x, t))

If the fractional derivative is taken for a product, the generalised Leibnitz rule is used to express the result (the product operator used is &* and is non-commutative). 
Rfracdiff(u(x, t)&*v(x,t),t,alpha);
     infinity                                                          
      -----                                                            
       \                                                               
        )                          (alpha - n)              n          
       /     binomial(alpha, n) D[t           ](u(x, t)) D[t ](v(x, t))
      -----                                                            
      n = 0                                                            
Rfracdiff(v(x, t)&*u(x,t),t,alpha);
     infinity                                                          
      -----                                                            
       \                                                               
        )                          (alpha - n)              n          
       /     binomial(alpha, n) D[t           ](v(x, t)) D[t ](u(x, t))
      -----                                                            
      n = 0                                                            

Fractional derivatives of integer order revert to the MAPLE diff routine.

Rfracdiff(u(x, t)&*v(x,t),t,2);
         / d  / d         \\             / d         \ / d         \
         |--- |--- u(x, t)|| v(x, t) + 2 |--- u(x, t)| |--- v(x, t)|
         \ dt \ dt        //             \ dt        / \ dt        /

                      / d  / d         \\
            + u(x, t) |--- |--- v(x, t)||
                      \ dt \ dt        //

The FracSym rouine TotalD may also be used to find total derivatives. evalTotalD is then used to evaluate the result (in jet notation). For example, 

TotalD(xi[x](x, y),x,2);
                                2              
                             D[x ](xi[x](x, y))
evalTotalD([%],[y],[x]);
        [     / d             \      2 / d  / d             \\
        [y_xx |--- xi[x](x, y)| + y_x  |--- |--- xi[x](x, y)||
        [     \ dy            /        \ dy \ dy            //

               / d  / d             \\       / d  / d             \\]
           + 2 |--- |--- xi[x](x, y)|| y_x + |--- |--- xi[x](x, y)||]
               \ dy \ dx            //       \ dx \ dx            //]

EXAMPLE -  FINDING SYMMETRIES FOR A FRACTIONAL DE

Consider the fractional PDE from: R. Sahadevan, T. Bakkyaraj, Invariant analysis of time fractional generalized Burgers and Korteweg-de Vries equations, J. Math. Anal. Appl. 393 (2012) 341-347.

We use the Rfracdiff routine to express the 
                                    alpha
 fractional derivative with respect to t:
fde1:=Rfracdiff(u(x, t),t,alpha) = (diff(u(x, t), x,x))+n*(u(x, t))^p*(diff(u(x, t),  x));
        alpha             / d  / d         \\            p / d         \
     D[t     ](u(x, t)) = |--- |--- u(x, t)|| + n u(x, t)  |--- u(x, t)|
                          \ dx \ dx        //              \ dx        /

sys1:=[Rfracdiff(u(x, t),t,alpha) = (diff(v(x, t), x)), Rfracdiff(v(x, t),t,alpha) = -u(x, t)*diff(u(x, t),x)];
[   alpha              d              alpha                      / d         \]
[D[t     ](u(x, t)) = --- v(x, t), D[t     ](v(x, t)) = -u(x, t) |--- u(x, t)|]
[                      dx                                        \ dx        /]

We use the the FracSym routine fracDet to find the determining equations for the symmetry for fde1. 
NOTE: The fourth argument (some integer at least 1) corresponds to the number of terms to be "peeled off" from the sums which occur in the extended infintesimal function for the fractional derivative. A value of 2 provides a good balance between information for solution of determining equations and speed.

deteqs:=fracDet([sys1], [u, v],[x, t], 2, alpha=(0.1)..1);
Error, (in desolv/PickLHSDerivative) Cannot pick out the left hand side derivatives

Please suggest what problem it may be?
 

Hi everyone, I'm doing a thesis about a solar panel and to extract some parameters from measured data I woudl have to solve 

a set of 3 non-lineair equations. This is de code that I use to (try to) solve the equations.

restart;

;
q := 0.16021e-18;
k := 0.13865e-22;


NULL;
Ns := 28;
T := 273+27.82;
Isc := 2.07;
Voc := 19.45;
Impp := 1.88;
Vmpp := 15.32;
                           Rsh := 326
dvdi := -1.52;


Vt := n*k*T*Ns/q;

NULL;
f1 := Rs = -dvdi-Vt/(Io*exp(Voc/Vt));
f2 := Io = (Isc-Voc/Rsh)/(exp(Voc/Vt)-1);
                            /Impp Rs + Vmpp\   Impp Rs + Vmpp
   f3 := Impp = Isc - Io exp|--------------| - --------------
                            \      Vt      /        Rsh      

fsolve({f1, f2, f3}, {Io, Rs, n});

Though running this doesn't give me a solution. 

I do have a working extraction though which is the same equations but with other variables: 

restart;

NULL;
q := 0.16021e-18;
k := 0.13865e-22;


NULL;
Ns := 72;
T := 298;
Isc := 8.53;
Voc := 44.9;
Impp := 8.04;
Vmpp := 36.1;
Rsh := 401.934;
dvdi := -.48766;


Vt := n*k*T*Ns/q;

NULL;
f1 := Rs = -dvdi-Vt/(Io*exp(Voc/Vt));
f2 := Io = (Isc-Voc/Rsh)/(exp(Voc/Vt)-1);
f3 := Impp = Isc-Io*(exp((Impp*Rs+Vmpp)/Vt)-1)-(Impp*Rs+Vmpp)/Rsh;

fsolve({f1, f2, f3}, {Io, Rs, n});

I'm am wondering why the first code doesn't give me a solution? I would guess that there is certainly a solution. Also when I slightly increase /  decrease a certain variable it can suddenly give/find a solution.

Could someone clear this out ?

Kind regards, Sven!

Why does the implicit plot return empty?

plots:-implicitplot((x^2+y^2 = 1)^2, x = -3 .. 3, y = -3 .. 3);# plots
   plots:-implicitplot((x^2+y^2-1)^2, x = -3 .. 3, y = -3 .. 3) # empty plot

I kind of work on generat asample from  Adiscret uniform distribution with pdf (P(x)=1/k+1  x=0..k). 
but i couldn't insert the PDF to generate asample is there any way to insert this pdf in maple then generata asample

So I currently have:
with(DifferentialGeometry); with(Tensor);
DGsetup([r, theta], pol);
g1 := evalDG(drdr+r^2d(theta)d(theta))
C1 := Christoffel(g1);
However its coming back saying that g1 is not of metric form, am i missing something? Thanks

Dear Maple users

I am trying to test how well data from a real throw with a ball comply with the usual model, in which the air resistance is proportional to the square of the velocity. I succeeded in solving the ODE system numericallly using the rkf45 method and plottet the solutioncurve (see attached file). I am however unsure how I can retrieve the data from the model in the most convenient way in order to compare them to the data from the real throw. The latter I have as (t, x(t), y(t)) data in three columns in an Excel file. Of course I can import the x og y columns into Maple and create a plot containing both the (x,y) data from Excel and the (x,y) data from the model. The problem is however that even if the (x,y) curves are rather close, if may not be a good model. I need to take into account the time variabel as well! The data from the Excel file contains data for every 1/30 second. What I like is to be able to compute the Root Mean Square of all (x_experiment(t)-x_model(t), y_experiment(t)-y_model(t)) data - or would the Root Mean Square of the (Euclid) distances between the points be better?

Now back to my question on how to retrieve data from the ODE system in the most convenient way. I have read the help page for the dsolve command. There is however several options, that I am unsure about, for example the output option (listprocedure, etc). I hope someone can help. 

NB! Excel data are imported column by column into Maple as n x 1 matrices.

Regards,

Erik V. 

Throw_with_air_resistance_1.mw