## Boundary Value Problem, some iteration without eva...

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PLS FIND ATTACHED A MAPLE CODE TO SOLVE SOME BOUNDARY VALUE PROBLEM, BUT IT JUMP SOME ITERATION WITHOUT EVALUATION WHICH END UP WITH INACCURATE SOLUTION.

> restart;
> with(LinearAlgebra);
> exp(1) := 2.7182818284590452354;
> alpha := .975;
> NULL;
> st := time[real]();
> for i to 4 do for j from 0 by .1 to 4-exp(1) do Exact[j] := evalf(ln(exp(1)+j)); Y[0] := proc (x) options operator, arrow; 1+x/exp(1)+(1/4)*((exp(1))^2-8*exp(1)+24*ln(2)*exp(1)-32)*x^2/(exp(1)*(16-8*exp(1)+(exp(1))^2))+(1/4)*(16*ln(2)*exp(1)-16-8*exp(1)+(exp(1))^2)*x^3/((-64+48*exp(1)-12*(exp(1))^2+(exp(1))^3)*exp(1)) end proc; Ics := Z(0) = 1, (D(Z))(0) = 1/exp(1), Z(4-exp(1)) = evalf(ln(4)), (D(Z))(4-exp(1)) = 1/4; f := proc (x) options operator, arrow; 0 end proc; p := proc (x) options operator, arrow; 0 end proc; q := proc (x) options operator, arrow; 0 end proc; r := proc (x) options operator, arrow; 0 end proc; u := proc (x) options operator, arrow; 0 end proc; eq[i] := diff(Z(x), $(x, 4)) = (1-alpha)*(diff(Y[i-1](x), $(x, 4)))+alpha*(-6*convert(taylor(exp(-4*Y[i-1](x)), x = 0, 20), polynom)); s[i] := dsolve({Ics, eq[i]}, Z(x)); Y[i] := unapply(op(2, s[i]), x); App[j] := evalf(Y[i](j)); Er[j] := abs(App[j]-Exact[j]); print([App[j], Exact[j], Er[j]]) end do end do; time[real]()-st;

## Use of ATLAS in calculation of Riemannian metric i...

I wish to calculate connection, curvature, Ricci curvature etc. for a

Riemannian metric given as follows: there is an orthogonal frame of vector

fields with stipulated Lie bracket relations between them. The frame is

orthogonal but not orthonormal, and the lengths of its vector fields are functions

of a single function on the manifold. Given these metric values on the frame and the

Lie bracket relations, the covariant derivatives are in principle computable from the

Koszul formula, hence connection and curvature are all determined.

When I try to define the metric using a dual coframe in ATLAS's Metric

routine, it allows me to define it but claims there is not actual curvature.

From the help it seems the coframes used in this routine are always given

as differentials of coordinates. Is there a way to get the metric via the data

given above without putting in by hand all the different Koszul formulas etc.?

## How to solve equation system?...

Hi,

i want to solve equation system u0(x,t),u1(x,t),v1(x,t),v0(x,t)v2(x,t) dependent on f(x,t).

I attached file.

worksheet.mwworksheet.mw

using worksheet mode, is there a way to automatically color any comments after (#) with a different color than the default red?

I have been using Maple for years and did not need to significantly document or comment on my worksheets before because I only needed to share my worksheets with close collegues who have a lot of experience with Maple too. However, now I need to share my code with a general audience that might not be a Maple user. So I need to add enough comments after each line, and I have been manually changing the color of comments after the # to green to give the reader the indication that this is a comment and not part of the code, like this for example:

 > restart;
 > f:=(x,y)->sin(sqrt(x^2+y^2))/sqrt(x^2+y^2); # Define f as a function of the variables x and y
 (1)
 > df:=(x,y)->eval(diff(f(a,y),a),a=x); # Define df as the partial derivative of f with respect to x
 (2)
 > df(1,3); # Evaluate df at x=1, y=3
 (3)
 >

It would be great if Maple can automatically color comments like typical editors do. Is this possible? if not, does anyone have an advice for a nice easy way to add proper documentation to worksheets?

## Trace in Physics package at Maple14...

I try to repeat lines (25)-(28) at

http://www.maplesoft.com/support/help/maple/view.aspx?path=Physics%2fTrace#commentform

I use Maple 14. However, instead of (28) I get the following result:

It means that Maple 14 does not perceive p_\mu, k_\nu and m as scalar quantities. I would like to ask how to define these variables correctly.

## Error when fsolving ...

Error, (in fsolve/polynom) Digits cannot exceed 38654705646

I am using fsolve to find numerical approximations to the roots of many fairly large polynomials (degrees up to ~80).  I often get this error message and I'm not sure why.  Is there any workaround?  Any help is much appreciated.

hi friends

I encountered a problem and I can not draw the plot of this code

> sol := fsolve({diff(S, x) = 0, diff(S, y) = 0}, {x, y});

> with(VectorCalculus);
> with(linalg);
> s1 := evalf(subs(sol, linalg[grad](S, [x, y])));

> with(VectorCalculus);
> with(LinearAlgebra);
> s2 := evalf(subs(sol, linalg[hessian](S, [x, y]))); pmp0 := [x-subs(sol, x), y-subs(sol, y)]; sapprox := s0+evalm(&*(&*(transpose(pmp0), s2), pmp0));
> with(Statistics);
>
> with(stats); statevalf[icdf, chisquare[4]](.95);

> with(VectorCalculus);
> with(plottools);
> with(plots);
> with(linalg); ellips := {seq(stats*([statevalf[icdf, chisquare[4]]])(c) = sapprox, c = [.5, .95, .999])};
> plots(ellips(x, y), x = 950 .. 1000, y = 700 .. 750, grid = [50, 50], view = [950 .. 1000, 700 .. 750]);

can you helpe me?Thank you

## Error, invalid input: with expects...

hi friends

After this cods i see very error

> restart;

ax := -G*Mz*x/(x^2+y^2)^(3/2);
ay := -G*Mz*y/(x^2+y^2)^(3/2);
i := 'i'; j := i+1;
for k from 0 to 3 do
x := 7*10^6; Vx := 0;
y := 0; Vy := 9000;
dt := evalf(1/2^k);
for i from 0 to 328 do
X[i] := evalf(x); Y[i] := evalf(y);
for n to 40*2^k do
x := evalf((1/2)*ax*dt^2+Vx*dt+x); y := evalf((1/2)*ay*dt^2+Vy*dt+y);
Vx := evalf(ax*dt+Vx); Vy := evalf(ay*dt+Vy)
od;
if i mod 41= 0 then
dX[k, i] := X[i]-XS[j]; dY[k, i] := Y[i]-YS[j]
fi
od;
p[k] := plot([seq([(X[i]-XS[j])*(1/1000), (Y[i]-YS[j])*(1/1000)], i = 0 .. 328)], color = green) end do;
p1 := display({seq(p[k], k = 0 .. 3)}, thickness = 3)
SI := [seq(41*i, i = 0 .. 8)]
p2 := plot({seq([seq([(1/1000)*dX[k, i], (1/1000)*dY[k, i]], k = 0 .. 1), [0, 0]], i = SI)}, color = black)
display({p1, p2}, scaling = constrained, labels = ['dx', 'dy'])
display({p1, p2}, view = [-.1 .. .5, -.4 .. .2], scaling = constrained, labels = ['dx', 'dy'])

Thank you

## How we use Gamma function...

Hi!

Please find my Maple-worksheet attached below.

How do I solve this problem? I can not drawn it.

I would really appriciate if somebody could help me.

## How i substitute variables in a Sum i=1,..i=100 fr...

Dear all

I want your help in a problem.I want to substitute in a summarization ,the variables for Vi and ξi.Because the number of variables are more than 200 I want to know if there is a way to take them from the excel sheet and put the to my program.attached are the maple worksheet and the variables table

P.s. i have done it for 44 variables

## i need the answer ASAP for my test, ty...

write down the mapple procedure that finds the shape operator plus
gauss and primative curvatores and determines the surface characteristic
of a parametically given surface

best regards, ty

## error on solving diffrential equation...

I am running a set of diffrential equation , but i receive below error

"Error, (in LL) cannot evaluate the solution past the initial point, problem may be complex, initially singular or improperly set up"

I can't understand the problem

## how do I solve a distinct-degree decomposition pro...

Trace  on computing the distinct-degree decomposition of the squarefree polynomial
f=x^17+2x^15+4x^13+x^12+2x^11+2x^10+3x^9+4x^4+3x^3+2x^2+4x belong to F_5[x].tell from the output only how many irreducible factors of degree i the polynomial f has, for all i.

## Help calling Matlab R2012b from Maple 14 on macos ...

Hello,

I was wondering if I can call Matlab R2012b with maple 14 on my macos 10.7.5.

When I try to do this:

> Matlab[setvar]("x", 3.14);

I get this:

I read that I may have to change a script. Where are those scripts located?

Regards,

## how to do a point plot if there is a range in valu...

Hi there..

I have a question on how to do a pointplot.

before plotting, I need to know the value of lambda[j] and  all the values of lambda already have.

so now I need to plot a graph with the values of lambda with different range and different colour,

Let say I have

> for j from 17 to 32 do k[j] := j+1;

x[j] := add(P[j, 1], j = j-1 .. j+2);

X[j] := add(P[j, 1]^2, j = j-1 .. j+2);

y[j] := add(P[j, 2], j = j-1 .. j+2);

Y[j] := add(P[j, 2]^2, j = j-1 .. j+2);

xy[j] := add(P[j, 1]*P[j, 2], j = j-1 .. j+2);

cx[j] := evalf(x[j]/k[j]);

cy[j] := evalf(y[j]/k[j]);

c11[j] := evalf(X[j]/k[j]-cx[j]^2);

c22[j] := evalf(Y[j]/k[j]-cy[j]^2);

c12[j] := evalf(xy[j]/k[j]-cx[j]*cy[j]);

C[j] := evalf(Matrix(2, 2, [[c11[j], c12[j]], [c12[j], c22[j]]]));

E[j] := simplify(fnormal(LinearAlgebra[Eigenvalues](C[j])));

if E[j][1] > E[j][2] then lambda[j] := E[j][2]/(E[j][1]+E[j][2]) else lambda[j] := E[j][1]/(E[j][1]+E[j][2])  end if;

lambda[j];

end do;

the range of lambda [j] are as follows:

0.02< lambda [j]<0.06

0.06< lambda [j]<0.12

0.12< lambda [j]<0.18

for i from 17 to 32, do if   0.02< lambda [j]<0.06 then green[i]:=P[i,j]; j:=i+1 elif

0.06< lambda [j]<0.12 then red[i]:=P[i,j];j:=i+1 ; elif 0.12< lambda [j]<0.18 then blue[i]:=P[i,j];j:=i+1 end if;end do

how to do a point plot with the above situation so that in my plotting all the information are on the same graph.

All help is greatly appreciated.

Thanks

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