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How to solve delay differential equations with Maple?


diff(x(t),t) = 3*x(t)^2 + 0.3*x(x-0.03)

Hey there,

I've a numerical solved system of differential equations, which depend on one argument and one index. I can solve it, but when I try plot it I have this error: Error, (in plot) two lists or Vectors of numerical values expected.

Could anyone help me figure out what I'm doing wrong?


> restart;
> A := 115.1558549; B := .3050464658; n := 3; f0 := 0.5e-4;

> alpha := [0, 1, 2, 3, 4, 5, 6];

Theta := [3*Pi*(1/180), 6*Pi*(1/180), 9*Pi*(1/180), 12*Pi*(1/180), 15*Pi*(1/180), 18*Pi*(1/180), 21*Pi*(1/180), 24*Pi*(1/180), 27*Pi*(1/180), 30*Pi*(1/180), 33*Pi*(1/180), 36*Pi*(1/180), 39*Pi*(1/180), 42*Pi*(1/180), 45*Pi*(1/180), 48*Pi*(1/180), 51*Pi*(1/180), 54*Pi*(1/180), 57*Pi*(1/180), 60*Pi*(1/180)];

>G:= theta->A*sin(theta)*cos(2*arcsin((sin(theta)/n)))/((1+sin(theta)^2/B^2)*cos(arcsin(sin(theta)/n)));

>for j from 1 to 7 do
d1 := diff(Ir(z), z) = -sum(G(Theta[k])*Ir(z)*Is[k](z)/I0,k=1..20)-alpha[j]*Ir(z)-sum(f(Theta[k])*Ir(z),k=1..20):
d2 := diff(Is[1](z), z) = G(Theta[1])*Ir(z)*Is[1](z)/I0-alpha[j]*Is[1](z)+f(Theta[1])*Ir(z):
d3 := diff(Is[2](z), z) = G(Theta[2])*Ir(z)*Is[2](z)/I0-alpha[j]*Is[2](z)+f(Theta[2])*Ir(z):
d4 := diff(Is[3](z), z) = G(Theta[3])*Ir(z)*Is[3](z)/I0-alpha[j]*Is[3](z)+f(Theta[3])*Ir(z):
d5 := diff(Is[4](z), z) = G(Theta[4])*Ir(z)*Is[4](z)/I0-alpha[j]*Is[4](z)+f(Theta[4])*Ir(z):
d6 := diff(Is[5](z), z) = G(Theta[5])*Ir(z)*Is[5](z)/I0-alpha[j]*Is[5](z)+f(Theta[5])*Ir(z):
d7 := diff(Is[6](z), z) = G(Theta[6])*Ir(z)*Is[6](z)/I0-alpha[j]*Is[6](z)+f(Theta[6])*Ir(z):
d8 := diff(Is[7](z), z) = G(Theta[7])*Ir(z)*Is[7](z)/I0-alpha[j]*Is[7](z)+f(Theta[7])*Ir(z):
d9 := diff(Is[8](z), z) = G(Theta[8])*Ir(z)*Is[8](z)/I0-alpha[j]*Is[8](z)+f(Theta[8])*Ir(z):
d10 := diff(Is[9](z), z) = G(Theta[9])*Ir(z)*Is[9](z)/I0-alpha[j]*Is[9](z)+f(Theta[9])*Ir(z):
d11 := diff(Is[10](z), z) = G(Theta[10])*Ir(z)*Is[10](z)/I0-alpha[j]*Is[10](z)+f(Theta[10])*Ir(z):
d12 := diff(Is[11](z), z) = G(Theta[11])*Ir(z)*Is[11](z)/I0-alpha[j]*Is[11](z)+f(Theta[11])*Ir(z):
d13 := diff(Is[12](z), z) = G(Theta[12])*Ir(z)*Is[12](z)/I0-alpha[j]*Is[12](z)+f(Theta[12])*Ir(z):
d14 := diff(Is[13](z), z) = G(Theta[13])*Ir(z)*Is[13](z)/I0-alpha[j]*Is[13](z)+f(Theta[13])*Ir(z):
d15 := diff(Is[14](z), z) = G(Theta[14])*Ir(z)*Is[14](z)/I0-alpha[j]*Is[14](z)+f(Theta[14])*Ir(z):
d16 := diff(Is[15](z), z) = G(Theta[15])*Ir(z)*Is[15](z)/I0-alpha[j]*Is[15](z)+f(Theta[15])*Ir(z):
d17 := diff(Is[16](z), z) = G(Theta[16])*Ir(z)*Is[16](z)/I0-alpha[j]*Is[16](z)+f(Theta[16])*Ir(z):
d18 := diff(Is[17](z), z) = G(Theta[17])*Ir(z)*Is[17](z)/I0-alpha[j]*Is[17](z)+f(Theta[17])*Ir(z):
d19 := diff(Is[18](z), z) = G(Theta[18])*Ir(z)*Is[18](z)/I0-alpha[j]*Is[18](z)+f(Theta[18])*Ir(z):
d20 := diff(Is[19](z), z) = G(Theta[19])*Ir(z)*Is[19](z)/I0-alpha[j]*Is[19](z)+f(Theta[19])*Ir(z):
d21 := diff(Is[20](z), z) = G(Theta[20])*Ir(z)*Is[20](z)/I0-alpha[j]*Is[20](z)+f(Theta[20])*Ir(z):
dsys := {d1, d10, d11, d12, d13, d14, d15, d16, d17, d18, d19, d2, d20, d21, d3, d4, d5, d6, d7, d8, d9}:
dSol[j] := dsolve({op(dsys), Ir(0) = 1, Is[1](0) = 0.1e-1, Is[2](0) = 0.1e-1, Is[3](0) = 0.1e-1, Is[4](0) = 0.1e-1, Is[5](0) = 0.1e-1, Is[6](0) = 0.1e-1, Is[7](0) = 0.1e-1, Is[8](0) = 0.1e-1, Is[9](0) = 0.1e-1, Is[10](0) = 0.1e-1, Is[11](0) = 0.1e-1, Is[12](0) = 0.1e-1, Is[13](0) = 0.1e-1, Is[14](0) = 0.1e-1, Is[15](0) = 0.1e-1, Is[16](0) = 0.1e-1, Is[17](0) = 0.1e-1, Is[18](0) = 0.1e-1, Is[19](0) = 0.1e-1, Is[20](0) = 0.1e-1}, [Ir(z), Is[1](z), Is[2](z), Is[3](z), Is[4](z), Is[5](z), Is[6](z), Is[7](z), Is[8](z), Is[9](z), Is[10](z), Is[11](z), Is[12](z), Is[13](z), Is[14](z), Is[15](z), Is[16](z), Is[17](z), Is[18](z), Is[19](z), Is[20](z)], numeric);
end do:

>for j from 1 to 7 do
for l from 1 to 20 do

Error, (in plot) two lists or Vectors of numerical values expected

How to find the determining equation for a system of fractional differential equation using Maple 15?


I want to write a proc to calculate exponential averages. Each call will add one data point to the averge. To do that, I need to store the previous average. I can do that by handing the previous average back to the proc at the next call, but I'd rather store it in the proc. Is there a way to guarantee that a variable---once set---remains alive keeping the last value upon entering the proc again? Note that I need the variable to be local to each instance of the proc since I will have several of these running in parallel (I intend to create these procs using the module factory scheme outlined in the programming guide). So I cannot store the previous average in a global variable since that would not be unique to a given instance.

Any ideas out there?


Mac Dude


Hello, I am newbie in Maple...

I tried to make a simple iteration, and I would like to get complex results for Z2, Z4 and Z5, as they have complex tag in them.

Would anybody to be so kind, to have a look at my file, and tell me, what's the mistake?

Thank you:


I use Maple 15 to calculate some (nasty) integrals at my university. Because our university also offers a server on which I can run my Maple program, I would like to do that. (instead of occupying a workspace). But at the computer on my workspace the integrals are evaluated fine, but on the server the integrals are just returned with no numerical evaluation.

I constructed a MWE to look where it goes wrong. I set the printlevel to 25 so I could see what was going on. The MWE was suprisingly simple, on both machines (via ssh) I executed within maple:

evalf(Int(1/sqrt(x), x=0..2))

This of course would normally just give 2*sqrt(2). On my workplace-pc it worked fine and it found 2.828427125. The server just returned the integral. After looking at the steps, they where both exactly the same until the following part:


         General_flags := {_NoNAG, _DEFAULT, _NoMultiple}

            NAG_methods := {_d01ajc, _d01akc, _d01amc}

                        Method := _DEFAULT

                          HFDigits := 15

                        HFeps := 0.1 10

                    HFeps := 0.5000000000 10

   oldEvents := overflow = default, division_by_zero = default

                         callNAG := true

                            fcns := {}

                  result := 2.82842712474618807


        General_flags := {_NoNAG, _DEFAULT, _NoMultiple}

           NAG_methods := {_d01ajc, _d01akc, _d01amc}

                       Method := _DEFAULT

                         HFDigits := 15

                       HFeps := 0.1 10

                   HFeps := 0.5000000000 10

   oldEvents := overflow = default, division_by_zero = default

                         callNAG := true

                           fcns := {}

       overflow = exception, division_by_zero = exception

It seems that the server has a problem with the singularity and thus throwing an exception, but I just don't get why. The Maple-versions are both the same.

Does somebody know what this could be?


dy/dt=y(9/4 -y^2)-(x^2)y 

What Maple15 commands will display a Rouleaux tetrahedron or a Meissner tetrahedron?


I got the Real and Imaginary of an expression J1 




J1mod:=simplify((Re(J1))^2+(Im(J1))^2): (I works here this amont is real)


but when I change the expression  for J1 to be



J1mod here is complex(I dont know why? it doesnt separate the real and the im )

Any comments will help


    Intersection of surfaces:

x3-.25*(sin(4*x1)+sin(3*x2+x3)+sin(2*x2))=0;  (1)

(x1-xx1)^4+(x2-xx2)^4+(x3-xx3)^4-1=0;          (2)   

   Surface (1) and a set of surfaces (2). Point (xx1, xx2, xx3) belongs to (1). Moving along the surface (1), we compute its intersection with the surface (2).
   The program is very simple and its algorithm can be used for many other combinations of equations.  

I need help on plotting in for loop.

> N := 10; h := 1/N;
> for i from 0 to 10 do x[i] := i*h; p1 := evalf(cos(x[i])) end do;
> f1 := [seq([x[i], p1], i = 1 .. N)];
> plot([cos(x), f1], x = 0 .. 1, y = 0 .. 1);

The above code gives me  cos x plot and line plot, but I want plot of points and cos x.

The classical Draghilev’s method.  Example of solving the system of two transcendental equations. For a single the initial approximation are searched 9 approximate solutions of the system.
x01 := -1.; x02 := 1.;

Hello everybody,

I am working on a somewhat complicated analytical problem, which includes the evaluation of the following (finite and singularity free) double integral (the stated numerical parameters may vary):

Int(exp(18.1818*(Int((0.579160e-1*sqrt(x)*Ei(1., 0.500000e-4*x)+(1072.23*(.999950-1.*exp(-0.500000e-4*x)))/sqrt(x))/sqrt(x), x = 1. .. eta))-9.10000*eta)/eta, eta = 1. .. 100.)

There are no unevaluated variables inside (all the e's are real exp()s). However, when putting it through evalf(), Maple returns it (after calculating for some time) unevaluated. I have no idea why, as a simple box sum should succeed.

Any input would be appreciated. Best regards,

  K. Reuther


P.S.: Raw expression for further deliberations

Int(exp(18.1818*(Int((0.579160e-1*sqrt(x)*Ei(1., 0.500000e-4*x)+(1072.23*(.999950-1.*exp(-0.500000e-4*x)))/sqrt(x))/sqrt(x), x = 1. .. eta))-9.10000*eta)/eta, eta = 1. .. 100.)

How can I plot a vertical line say x = a in Maple 15 worksheet?


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