This Question involves using dsolve(..., numeric) for an IVP specifed by a procedure. This is based on a Question asked earlier today. In this Question, I have no interest in how to solve this IVP or in why this solution technique fails. In the worksheet below, the odeplot command seems to get stuck in an infinite loop (I am not interested in why that happens), and I press the stop button (in the Standard GUI). Then, instead of the usual Warning, computation interupted message followed by a return to the command prompt, I get an informative message and the plot that has been computed so far. This seems like a very useful feature: to return the results computed so far after an interuption. Furthermore, those results are programmatically accessible. My Question is How is this done? How do you trap the stop button and return the results?

Download trap_stop_button.mw

restart;
odes:=diff(x1(t),t)*diff(x2(t),t$2)*sin(x1(t)*x2(t))+5*diff(x1(t),t$2)*diff(x2(t),t)*cos(x1(t)^2)+t^2*x1(t)*x2(t)^2=exp(-x2(t)^2),diff(x1(t),t$2)*x2(t)+diff(x2(t),t$2)*diff(x1(t),t)*sin(x1(t)^2)+cos(diff(x2(t),t$2)*x2(t))=sin(t);
ics:=x1(0)=1,D(x1)(0)=1,x2(0)=2,D(x2)(0)=2;
subs(diff(x1(t),t$2)=yp2,diff(x2(t),t$2)=yp4,diff(x1(t),t)=Y[2],diff(x2(t),t)=Y[4],x1(t)=Y[1],x2(t)=Y[3],{odes});
p:=proc(N,t,Y,YP)
local eqs,yp2,yp4;
YP[1]=Y[2];
YP[3]=Y[4];
eqs:=[yp2*Y[3]+yp4*Y[2]*sin(Y[1]^2)+cos(yp4*Y[3]) = sin(t), Y[2]*yp4*sin(Y[1]*Y[3])+5*yp2*Y[4]*cos(Y[1]^2)+t^2*Y[1]*Y[3]^2 = exp(-Y[3]^2)];
YP[2],YP[4]:=op(subs(fsolve(eqs,{yp2=1,yp4=2}),[yp2,yp4]));
end proc:
res:=dsolve(numeric,procedure=p,initial=array([1,1,2,2]),number=4,procvars=[x1(t),diff(x1(t),t),x2(t),diff(x2(t),t)],start=0,maxfun=0);
plots:-odeplot(res,[t,x1(t)],0..5,gridlines=true);

It's a long time to wait for the odeplot.

Any advice is appreciated.

How do I iterate starting from a given value. For example, I want to iterate a function F(x) evalf(solve(F(x)=-38)) so that the next value that F(x) uses is the solution to the previous?

Is there a way to convert this FDTD code into Maple

Hy(1 to M)=0;

Ex(1 to M+1)=0;

For t=1 to T,

Ex(1)=exp(-t);

For k=1 to M,

Hy(k)=Hy(k)-(Ex(k+1)-Ex(k));

end

For k=2 to M,

Ex(k)=Ex(k)-(Hy(k)-Hy(k-1));

end

end

Thanks in advance.

Hello, 

I want to solve and plot a multitime recurrence of the Samuelson Hicks Model (http://www.mathem.pub.ro/proc/bsgp-22/K22-gh-A84.pdf).

Feel free to share any tips that could help.

Thank you. 

hello every one

i need to solve this equation

> A1 := Matrix([[a11, a12, a13], [a12, a22, a23], [a13, a23, a33]]);
> A2 := Matrix([[A], [B], [C]]);
> A3 := Matrix([[15], [0], [0]]);
> eq := multiply(A1, A2)=A3;

> solve(eq, {A, B, C});

thank you :)

Hi, I'm tying to solve the ODE by variational iteration method, programme is running, but maple answer does'nt  match to origional answer, plz tell me the mistake?

ICs y(0)=y'(0)=y''(0)=1

VIM_2.mw

Hello everyone, 

In Maple8, I tried to plot this logistic map and an error occured (Error, (in Bifurcation) `plots` does not evaluate to a module).

What is wrong into this code?

Thank you

restart: with(plots):Warning, the name changecoords has been redefined

> Bifurcation := proc(initialpoint,xexpr,ra,rb,acc)
> local p1,hr,A,L1,i,j,phi:
> global r,L2:
> hr := unapply(xexpr,x);
> A := Vector(600):
> L1 := Vector(acc*500):
> for j from 1 to acc+1 do
> r := (ra + (j-1)*(rb-ra)/acc):
> A[1] := hr(initialpoint):
> for i from 2 to 500 do
> A[i] := evalf(hr(A[i-1])):
> end do:
> for i from 1 to 400 do
> L1[i+400*(j-1)] := [r,A[i+100]]:
> end do:
> end do:
> L2 := {seq(L1[i], i = 1..acc*400)}:
> p1 := plots:-pointplot(L2, 'symbol' = solidcircle, 'symbolsize' = 8, 'color' = blue):
> unassign('r'):
> return(p1):
> end proc:
> P1:= Bifurcation(1/2,r*x*(1-x),2.5,4,250):
>
Error, (in Bifurcation) `plots` does not evaluate to a module

Hello everyone!

Do you have any idea to solve and plot a 2-time logistic map:

x(t+ 1_\alpha)= r*x(t)*(1-x(t))  ,t=(t^1,t^2)  ?

Thank you

I want to reduce all solution of the equation sin(x)^2=1/4

restart:
sol:=solve(sin(x)^2=1/4, x, AllSolutions);

and

restart:
k:=combine((sin(x))^2);
sol:=solve(k=1/4, x, AllSolutions = true, explicit);
simplify(sol);

How can I reduce solution sol := -1/3*Pi*_B3+1/6*Pi+Pi*_Z3 ?

How can I get x= pi/6+k*pi and x= -pi/6+k*pi?

In Maple 11 we have:

> A := <a,b,c>:
> a := 1:  b := 2: c := 3:
> convert(A, list);
                                   [1, 2, 3]

In Maple 2015 we have:

> A := <a,b,c>:
> a := 1:  b := 2: c := 3:
> convert(A, list);
                                   [a, b, c]

Is that change really intended?

Hi all,

restart;#part1
epsilon:=5:Delta1:=2:Delta2:=-4: N1:=1000:
dsys :={diff(x(t),t)=-I*Delta1*x(t)+y(t)+epsilon, diff(y(t),t)=-I*Delta2*y(t)+x(t)*z(t), diff(z(t),t)=-2*(conjugate(x(t))*y(t)+conjugate(y(t))*x(t))};

res:=dsolve(dsys union {x(0)=2*I,y(0)=0,z(0)=1},numeric,output=listprocedure);

P1:=plots:-odeplot(res,[[t,Im(y(t))],[t,Re(x(t))]],0..2):

/ d
{ --- x(t) = -2 I x(t) + y(t) + 5,
\ dt

d
--- y(t) = 4 I y(t) + x(t) z(t),
dt

d ____ ____ \
--- z(t) = -2 x(t) y(t) - 2 y(t) x(t) }
dt /
tit:=sprintf("D1=%g,D2=%g",Delta1,Delta2);
"D1=2,D2=-4"
plots[odeplot](res,[[t,Im(y(t))]],0..200,axes=boxed,titlefont=[SYMBOL,14],font=[1,1,18],color=black,linestyle=1,tickmarks=[3, 4],font=[1,1,14],thickness=2,titlefont=[SYMBOL,12]);
Warning, cannot evaluate the solution further right of 90.013890, maxfun limit exceeded (see ?dsolve,maxfun for details)

when I increase the time give this msn:

Warning, cannot evaluate the solution further right of 90.013890, maxfun limit exceeded (see ?dsolve,maxfun for details)

Hello,

Today I've playied a bit with CellDecomposition from the RootFinding package and for one of the systems with which I've playied I got an error which seems to me to be a bug related.

In particular, 

with(RootFinding[Parametric]):

m := CellDecomposition([x^3-y^2 = 0, x^2+y^2-1 < 0], [x, y])

Error, (in RootFinding:-Parametric:-CellDecomposition) Segmentation Violation occurred in external routine

Did I make a mistake somewhere or Maple 2015.1 faild?

I am working on a problem involving sums in Maple and I find Maple's facilities lacking.

Specifically; I want to convert the square of a sum into a sum of squares plus the cross terms (which is a subtask of a larger problem). So I start with

sum(E[n],n=1..N)^2;

and immediately get stuck as I do not find any command that does anything with it. The expansion of this is known and easy to derive:

sum(E[n],n=1..N)^2 = sum(E[n]^2,n=1..N) + 2*sum(sum(E[m]*E[n],m=1..n-1),n=1..N);

Maple knows nothing about this relation. I have checked out packages like SumTools but have not found anything useful for this purpose. Quite some time ago I have had difficulty distributing a sum over the elements of its expression; this was answered here and involved a custom function.

Does a package exist that has these kinds of conversions, or do I need to roll my own? It seems a general enough issue that I would expect functions for this to exist.

TIA,

Mac Dude