I have a non-linear function to be optimized. It involves infinite sums. Maple plots the function so I can see where the minimum is. However the NLP solve keeps on evaluating without providing the solution. I have tried to write the function as a procedure but it does not work either.

I'd appreciate any suggestion

I have several maple worksheets (from the web) that have discussion blocks mixed within executable blocks.

All the executable blocks are delineated with a single '[' at the left while the discussion blocks do not.

How do I do this?

Tom Dean

So i got this code, im trying to iterate with jacobi and gaussseidel method.

H := HilbertMatrix(n, n, 1); b := Matrix(n, 1, proc (i) options operator, arrow; add(1/(i+j-1), j = 1 .. n) end proc); A := Matrix(n, 1, 1); Multiply(H, A); norm1H := norm(H, 1); norm2H := norm(H, 2); normHinf := norm(H, infinity); norm1b := norm(b, 1); norm2b := norm(b, 2); norminfb := norm(b, infinity); IterativeApproximate(H, initialapprox = Vector(n, 0), tolerance = 10^(-7), maxiterations = 10, method = gaussseidel)

But sadly no iteration gave me an answer, anyone knows wheres my mistake? i really help with this! 


thanks in advance

I wish to apply several i-j constraints to an optimization problem that involves minimizing a function x[i,j]. 

Does anyone know of a simple way to exclude values for i and j? For instance, how do we specify the conditions, i not equal to j, i is not equal to 1, etc.?

Thanks in advance!

Friends

I have plotted some figures and saved them yesterfay!

now once i opened them some nonsence digits appear on the figure! see the picture please. anyone has similar experience? how to solve it!

Dont make me disappointed maple! two days work is invain now !

> restart;
> with(plots); with(StringTools); with(plottools);
> INF := 999999999999999999999;
                     999999999999999999999
> NULL;
> MinoxAngle := 200; MikromaAngle := 350; MinicordAngle := 290; GamiAngle := 280; GamiFocal := 0.25e-1; SummitarDial := [1, 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 2, 2.2, 3, 4, 5, 6, 7, 10, 20, INF]; Minox35MLDial := [3, 4, 6, 10, 20, INF]; Minox35Angle := 100; MinicordDial := [.35, .4, .5, .6, .7, .8, .9, 1, 1.2, 1.5, 2, 3, 4, 8, INF]; Mini := nops(MinicordDial); MikromaDial := [.5, .6, .7, .8, .9, 1, 1.2, 1.5, 2, 2.5, 3.5, 6, INF]; MinoxLXDial := [.2, .24, .3, .4, .6, 1, 2, 30]; MinoxLXAngle := 270; GamiDial := [.5, .6, .7, .8, 1, 1.2, 1.5, 2, 3, 5, 99990000000000]; MinoxBDial := [8*(1/12), 10*(1/12), 1, 1.5, 2, 3, 6, INF]; MinoxBAngle := 270;
                              200
                              350
                              290
                              280
                             0.025
[1, 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 2, 2.2, 3, 4, 5, 6, 7, 10, 

  20, 999999999999999999999]
            [3, 4, 6, 10, 20, 999999999999999999999]
                              100
 [0.35, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1, 1.2, 1.5, 2, 3, 4, 8, 

   999999999999999999999]
                               15
    [0.5, 0.6, 0.7, 0.8, 0.9, 1, 1.2, 1.5, 2, 2.5, 3.5, 6, 

      999999999999999999999]
              [0.2, 0.24, 0.3, 0.4, 0.6, 1, 2, 30]
                              270
   [0.5, 0.6, 0.7, 0.8, 1, 1.2, 1.5, 2, 3, 5, 99990000000000]
         [2  5                                        ]
         [-, -, 1, 1.5, 2, 3, 6, 999999999999999999999]
         [3  6                                        ]
                              270
> 
> NULL;
> dd := GamiDial; N := nops(dd); dstx := [seq(convert(dd[i], string), i = 1 .. N)];
   [0.5, 0.6, 0.7, 0.8, 1, 1.2, 1.5, 2, 3, 5, 99990000000000]
                               11
  [".5", ".6", ".7", ".8", "1", "1.2", "1.5", "2", "3", "5", 

    "99990000000000"]
> NULL;
> MinicordAngle := 290;
                              290
> NULL;
> 
> LensDial := proc (LensName, focal, Angle, scale, dr) local p1, p2, p3, p8, pk, pt, rk, R, R2, R3, Rc, c1, ds2; R := 1600; R2 := 1400; R3 := 1200; Rc := 1500; CaptionTail1 := "EXTENSION ANGLE"; CaptionTail2 := "LENS FOCUSING DIAL"; Caption1 := Join([LensName, CaptionTail1]); Caption2 := Join([LensName, CaptionTail2]); q := 180/Pi; rotation := 90; dir := dr; ds := scale; N := nops(ds); dstx := [seq(convert(ds[i], string), i = 1 .. N)]; ds2 := subs(dstx[N] = infinity, dstx); MaxAngle := Angle; f := focal; degr := -(-ds[1]+f)*Angle/(D-f)+rotation; g1 := degr/q; for j to N do deg[j] := subs(D = ds[j], degr) end do; for i to N do rdn[i] := evalf(deg[i]/q); xv[i] := R2*cos(rdn[i]); yv[i] := R2*sin(rdn[i]); wx[i] := R3*cos(rdn[i]); wy[i] := R3*sin(rdn[i]) end do; pk := {seq([ds[i], deg[i]], i = 1 .. N)}; rk := {seq([dir*xv[i], yv[i]], i = 1 .. N)}; txt := {seq([dir*wx[i], wy[i], ds2[i]], i = 1 .. N)}; p3 := pointplot(rk, caption = Caption2, captionfont = ["ROMAN", bold, 22], symbol = solidcircle, symbolsize = 15, color = red, axes = none); c1 := circle([0, 0], Rc, thickness = 8); p8 := textplot(txt, 'font' = ["times", "bold", 14]); display(p3, c1, p8, scaling = constrained) end proc;
Warning, `CaptionTail1` is implicitly declared local to procedure `LensDial`
Warning, `CaptionTail2` is implicitly declared local to procedure `LensDial`
Warning, `Caption1` is implicitly declared local to procedure `LensDial`
Warning, `Caption2` is implicitly declared local to procedure `LensDial`
Warning, `q` is implicitly declared local to procedure `LensDial`
Warning, `rotation` is implicitly declared local to procedure `LensDial`
Warning, `dir` is implicitly declared local to procedure `LensDial`
Warning, `ds` is implicitly declared local to procedure `LensDial`
Warning, `N` is implicitly declared local to procedure `LensDial`
Warning, `dstx` is implicitly declared local to procedure `LensDial`
Warning, `MaxAngle` is implicitly declared local to procedure `LensDial`
Warning, `f` is implicitly declared local to procedure `LensDial`
Warning, `degr` is implicitly declared local to procedure `LensDial`
Warning, `g1` is implicitly declared local to procedure `LensDial`
Warning, `j` is implicitly declared local to procedure `LensDial`
Warning, `deg` is implicitly declared local to procedure `LensDial`
Warning, `i` is implicitly declared local to procedure `LensDial`
Warning, `rdn` is implicitly declared local to procedure `LensDial`
Warning, `xv` is implicitly declared local to procedure `LensDial`
Warning, `yv` is implicitly declared local to procedure `LensDial`
Warning, `wx` is implicitly declared local to procedure `LensDial`
Warning, `wy` is implicitly declared local to procedure `LensDial`
Warning, `txt` is implicitly declared local to procedure `LensDial`
> ;
> NULL;
> LensDial("MEOPTA MICROMA  HELGOR 25mm", 0.25e-1, 350, MikromaDial, 1);

> LensDial("GOERZ MINICORD  25mm", 0.25e-1, 335, MinicordDial, 1);

> 
> ;
> LensDial("MINOX LX MINOX 15mm", 0.15e-1, 270, MinoxLXDial, 1);

> LensDial("GAMI ESAMITAR 25mm", 0.25e-1, 290, GamiDial, 1);

Hi,

I have a second order, linear, non-homogeneous differential equation and for the solution Maple takes the particular solution under a indefinite integral form. After I substitute the values of the coefficients I want Maple to perform the integration. The integration is possible because I individually integrated one small part of the expression. The full expression has a lenghty sumation of different indefinite integrals so it would be cumbersome to perform each integration by hand.

Can somebody help me force Maple to perform these integrations?

I already tried eval, evalf, simplfy and it doesn't work.

Thanks a lot.

hi

why this equation does not any answer?

thanks

s-s.mw
 

Download s-s.mw

Hi guys,

I run my code and after a point all the numerical values are followed by a dot. Why is that? Also the symbolic variables have a 1. before them.

Thanks a lot!

Hello! Hope everyone would be fine. I want to solve the following system of ODEs please help to find the numerical solution

N := .6; alpha := .4; beta := .1; Nt := .2; Pr := .5; Nb := .1; s := .2; lambda[1] := 1; delta := .5; gm := 1; Sc := 1:L:=1:

Eq1 := (alpha*s+1)*(diff(F(eta), eta, eta, eta))-(F(eta)+(1/2)*s*eta)*(diff(F(eta), eta, eta))+((1/2)*(diff(F(eta), eta))-s)*(diff(F(eta), eta))-2*(G(eta)^2-(1-gm)^2)-2*lambda[1]*(H(eta)+N*Y(eta))-(alpha+beta-(1/4)*delta*(diff(F(eta), eta, eta, eta)))*(diff(F(eta), eta, eta))^2-(alpha-2*beta)*(diff(F(eta), eta))*(diff(F(eta), eta, eta, eta))-(2*(alpha-beta-(1/4)*delta*(diff(F(eta), eta, eta, eta))))*(diff(G(eta), eta))^2-(2*(alpha-(1/4)*delta*(diff(F(eta), eta, eta))))*G(eta)*(diff(G(eta), eta, eta)) = 0; Eq2 := (alpha*s+1)*(diff(G(eta), eta, eta))-F(eta)*(diff(G(eta), eta))+G(eta)*(diff(F(eta), eta))+s*(1-gm-G(eta)-(1/2)*eta*(diff(G(eta), eta)))-(1/2)*alpha*s*eta*(diff(G(eta), eta, eta, eta))+((3/2)*alpha+beta)*G(eta)*(diff(F(eta), eta, eta, eta))-((1/2)*alpha+beta)*(diff(F(eta), eta))*(diff(G(eta), eta, eta))-delta*((diff(F(eta), eta, eta))^2+6*(diff(G(eta), eta))^2)*(diff(G(eta), eta, eta)) = 0; Eq3 := (diff(H(eta), eta, eta))/Pr-F(eta)*(diff(H(eta), eta))+(1/2)*H(eta)*(diff(F(eta), eta))-s*(2*H(eta)+(1/2)*eta*(diff(H(eta), eta)))+Nb*(diff(H(eta), eta))*(diff(Y(eta), eta))+Nt*(diff(H(eta), eta))^2 = 0; Eq4 := (diff(Y(eta), eta, eta))/Sc-F(eta)*(diff(Y(eta), eta))+(1/2)*Y(eta)*(diff(F(eta), eta))-s*(2*Y(eta)+(1/2)*eta*(diff(Y(eta), eta)))+Nt*(diff(H(eta), eta, eta))/Nb = 0;

IC1 := F(0) = 0, (D(F))(0) = 0, G(0) = gm, H(0) = 1, Y(0) = 1; IC2 := (D(F))(L) = 0, G(L) = 1-gm, (D(G))(L) = 0, H(L) = 0, Y(L) = 0; dsys1 := {Eq1, Eq2, Eq3, Eq4, IC1, IC2}; dsol1 := dsolve(dsys1, numeric, output = listprocedure, range = 0 .. L);

dsol1f := subs(dsol1, F(eta));

dsol1g := subs(dsol1, G(eta)); dsol1h := subs(dsol1, H(eta)); dsol1y := subs(dsol1, Y(eta));

With my best regards and sincerely.

Hi,

Seem to be a bit stuck. Here's my code:
 

Thanks in advance :-) 

Hi!

Everyone,

I want to draw  phase plane of system of three fractional order equations. 

Note that 

Also want the  phase portrait when the values of alpha are not same....

Also

Thanks

When print a formula , if variable has power, the power will print in another row

how can it print like a^2 in one row 

Here is one that the students generated which caused confusion. 

a := 0.76;
eq1 := 2*cot(a*sqrt(2*E)) = (2*E-5.4)/(sqrt(E*(5.4-E));
solve(eq1, E)

And the results are: 0., 4.411954070, 2.423743792

The problem is with the second answer because it does not exist. If we plot the LHS and the RHS of eq1 vs E where E=0..5.4

And it gets more interesting, if we calculate:

solve(evalf(eq1), E)

The answers are: 0., 2.423743793, 14.33807304+27.39159712*I

where the 3rd answer is again incorrect.

Finally, if a = 0.8 or larger, the incorrect answers disappear. 

Note - fsolve does handle this problem correctly. And despite my attempts to remind them to use fsolve, they see the solve command as the universal truth. Apparently this will be another teaching moment for next year.

So any thoughts about why this happens and why there is a difference in the outcomes between 0.76 and 0.8 for the value of a?

hi.

how i can dsolve this differential equations?

thanks

ich.mw
 

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