GambiaMan

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8 years, 281 days

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These are questions asked by GambiaMan

Hello,

I have an issue with this code. The issue lies in the warning which is outputed. However, I don't know how to resolve it. Any help would be greatly appreciated! Thank you in advance!

Kind regards,

Gambia Man

with(plots):

a := 1.501*10^9:

Eqns := diff(xH(t), t) = vxH(t), diff(vxH(t), t) = -G*(Mh+Msat)*xH(t)/(xH(t)^2+yH(t)^2)^(3/2), diff(yH(t), t) = vyH(t), diff(vyH, t) = -G*(Mh+Msat)*yH(t)/(xH(t)^2+yH(t)^2)^(3/2):

ICs := xH(0) = a*(1+e), yH(0) = 0, vxH(0) = 0, vyH(0) = sqrt(G*(Mh+Msat)*(1-e)/(a*(1+e))):

T := sqrt(4*Pi^2*a^3/(G*(Mh+Msat))):

soln := dsolve({Eqns, ICs}, numeric):

plots:-odeplot(soln, [xH(t)/a, yH(t)/a], 0 .. 10*T, scaling = constrained, labels = ["x/a", "y/a"], numpoints = 2000);

Warning, cannot evaluate the solution further right of 453574.15, probably a singularity

 

 

``

 

Download Hyperion_Orbit.mw

 

Hello,

I've got this error in my code and I don't know why as I didn't get it when I used a different xn function. Any help would be greatly appreciated! Thank you in advance!

Kind regards,

Gambia Man

restart

with(plots):

boxcount := proc (data, N) local n, xmax, xmin, xrange, ymax, ymin, yrange, dx, dy, i, j, ix, iy, sum, res; n := (1/2)*ArrayNumElems(data); xmax := max(seq(data[i, 1], i = 1 .. n)); xmin := min(seq(data[i, 1], i = 1 .. n)); ymax := max(seq(data[i, 2], i = 1 .. n)); ymin := min(seq(data[i, 2], i = 1 .. n)); xrange := xmax-xmin; xmin := xmin+(-1)*0.1e-1*xrange; xmax := xmax+0.1e-1*xrange; xrange := 1.02*xrange; yrange := ymax-ymin; ymin := ymin+(-1)*0.1e-1*yrange; ymax := ymax+0.1e-1*yrange; yrange := 1.02*yrange; dx := xrange/N; dy := yrange/N; res := Array(0 .. N-1, 0 .. N-1, 0); for i to n do ix := trunc((data[i, 1]-xmin)/dx); iy := trunc((data[i, 2]-ymin)/dy); res[ix, iy] := 1 end do; add(add(res[i, j], i = 0 .. N-1), j = 0 .. N-1) end proc:

``

bicationplot := proc (N) local Nr, Nt, x0, rmin, rmax, bif, k, ir, r, xn, i; global pts; Nr := 100; Nt := 200; x0 := .1; rmin := .75; rmax := 3.5; bif := Array(1 .. Nr*N, 1 .. 2); k := 1; for ir to Nr do r := rmin+ir*(rmax-rmin)/Nr; xn := x0; for i to Nt do xn := xn^2-r end do; for i to N do xn := xn^2-r; bif[k, 1] := r; bif[k, 2] := xn; k := k+1 end do end do; pts := bif end proc:

bif

bif

(1)

fractaldimension := proc (Noofitterations::integer, Npoints::integer, Nmax::integer) local res, xv, yv, line, stderrors, avgstderrors, i, avgline; avgstderrors := 0; avgline := 0; for i to Noofitterations do bicationplot(Npoints); res := [seq([1.0/n, boxcount(pts, n)], n = 1 .. Nmax, 10)]; xv := [seq(log(res[i][1]), i = 1 .. nops(res))]; yv := [seq(log(res[i][2]), i = 1 .. nops(res))]; line[i] := Fit(m*x+const, xv, yv, x, output = [leastsquaresfunction]); stderrors[i] := Fit(m*x+const, xv, yv, x, output = standarderrors) end do; for i to Noofitterations do avgstderrors := avgstderrors+stderrors[i] end do; avgstderrors := avgstderrors/Noofitterations; for i to Noofitterations do avgline := avgline+line[i] end do; avgline := avgline/Noofitterations; return FD = -(diff(avgline, x)), avgline, avgstderrors, loglogplot(res) end proc:

fractaldimension(10, 100, 100)

Error, (in boxcount) bad index into Array

 

``

 

Download First_part_fractal_determination_.mw

Hello,

I'm having some issues with this procedure it seems to take a very long time to evaluate. There is also an error in the Histogram I can't seem to fix... Does anybody know why? Any help would be greatly appreciated! Thank you in advance!

Kind regards,

Gambia man

Last_part2.mw

Hello,

I would like to know how to order a sequence of number from smallest to largest. This is if I have both real and imaginary numbers. Any help would be rgeatly appreciated! Thank you in advance.

Kind regards,

Gamiba Man

Hello,

I'm having an issue with this and I can't seem to fix it. Any help is greatly appreciated! Thank you in advance!!! For some reason mapleprimes won't let me upload the worksheet so I have pasted it below this message.

 

Kind regards.

Gambia Man

with(LinearAlgebra); UseHardwareFloats; with(plots); interface(rtablesize = infinity); with(Statistics);
L := 4; U := 1;
V := proc (x, y) options operator, arrow; piecewise((1/4)*L <= x and x <= (1/2)*L and (1/4)*L <= y and y <= (1/2)*L, U) end proc;
plot3d(V(x, y), x = 0 .. L, y = 0 .. L);

Vij := proc (ni, mi, nj, mj) local Xi, Xj; option remember; global U, L; Xi := 2*sin(ni*evalf(Pi)*x/L)*sin(mi*evalf(Pi)*y/L)/L; Xj := 2*sin(nj*evalf(Pi)*x/L)*sin(mj*evalf(Pi)*y/L)/L; return U*(int(int(Xi*Xj, x = (1/4)*L .. (1/2)*L), y = (1/4)*L .. (1/2)*L)) end proc;
HamilMat := proc (K::integer) local ni, mi, nj, mj, N, Hamil, Eigenvec, i, j, res; option remember; global Vij, U, L; N := K^2; ni := Vector(N); mi := Vector(N); nj := Vector[row](N); mj := Vector[row](N); for i to N do for j to K do res := (i+K-j)/K; if type(res, integer) = true then ni[i] := j; nj[i] := j; mi[i] := res; mj[i] := res end if end do end do; Hamil := Matrix(N, shape = symmetric); for i to N do for j from i to N do if i <> j then Hamil(i, j) := Vij(ni[i], mi[i], nj[j], mj[j]) elif i = j then Hamil(i, j) := Vij(ni[i], mi[i], nj[j], mj[j])+(1/2)*(ni[i]^2+mi[i]^2)*Pi^2/L^2 end if end do end do; Eigenvec := Eigenvectors(Hamil, output = ['values', 'vectors']), Hamil end proc;
SigFigEi := proc (Location::integer, SigFig::integer, VecSize::integer) local values, Eig, i; global HamilMat, OptK; Eig := Vector(VecSize); for i from 2 to VecSize do Eig[i] := HamilMat(i)[1][Location]; if evalf(Eig(i), SigFig+1) = evalf(Eig(i-1), SigFig+1) then OptK := i; break end if end do; values := evalf(Eig[i], SigFig); return values, OptK end proc;
BasisFunc := proc (location) local ni, mi, func, i, j, p, N, res, BasisSol; global HamilMat, L, OptK; p := evalf(Pi); N := OptK^2; ni := Vector(N); mi := Vector(N); for i to N do for j to OptK do res := (i+OptK-j)/OptK; if type(res, integer) = true then ni[i] := j; mi[i] := res end if end do end do; func := Vector(N); for i to N do func[i] := HamilMat(OptK)[2][i][location]*sin(ni[i]*p*x/L)*sin(mi[i]*p*y/L) end do; BasisSol := unapply(add(func[i], i = 1 .. N), x, y); return plot3d(BasisSol(x, y), x = 0 .. L, y = 0 .. L), func end proc;
BasisFunc(1);
Error, (in Vector) dimension parameter is required for this form of initializer

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