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Dear friends,

 

I have a huge differential equation which I am trying to solve.

However, even solving it numerically, maple keeps evaluating it for a long time and then stops working! So there is no solution.

I just want to check if there is any solution to this differential equation at all!

Do you know a way with which maple can check if the differential equation is solvable?

 

I am interested in dynamic systems that changes system equations at a given point in time. So i often want to plot graphs that shows what would happen in the first 500 seconds, then using the point reached after 500 seconds as the starting point show what happens over the next 500 seconds.

For example my equations might innitially

diff(x,t)=x+p*y

diff(y,t)=x/y

and then after 500 seconds switch to 

diff(x,t)=x-p*y

diff(y,t)=x/y

simply estimating where the system is and feeding that into the other equation isn't an option because these equations have lots of parameters which p is representing in the above, and generally i want too use these graphs to illustrate the behaveious of the systems with the given parameters.

So far i use display and DEplot to make these grpahs.

Non dimensionalisation is a vary common task, and I was suprised that I couldn't find a maple tool to automate it . Has anyone developed their own package for it?

I want to automatically do it to the system equations for some Dynamical systems to make some of the other processing I do with them easier.

I was hoping to start with somehting in the form of 

Diff(x[1],t)=f[1](p[1]....p[n],x[1]...x[m])

...

Diff(x[m],t)=f[m](p[1]....p[n],x[1]...x[m])

where each f[i] is some kind of quotient of multivariate polynomials in the variables and parameters:
and end up with something like

Diff(y[1],s)=f[1](q[1]....q[p],y[1]...y[m])

...

Diff(y[m],s)=f[m](q[1]....q[p],y[1]...y[m])

where p<n


 

Download inf2.mw

hello

 

i write this set of differential equation in maple and get the following error?

Can anyon help me with this?

 

thanks

 

 

I want to solve an ODE from Game Theory, the Cournot competition.

It says

p(q1+r2(q1))+p'(q1+r2(q1))*r2(q1)-c2'(r2(q1))=0

 where, I think,

' means diff(,q1),

c2(q2)=c*q2 for a fixed c in [0,1]

and

p(q)=max(0,1-q).

So c2,p and r2 are functions.r2 goes from [0,inf) to [0,inf).

I look for r2, which should be r2(q1)=(1-q1-c)/2 when correctly solved.

However, the command dsolve says Error in dsolve (divison by 0).

 What is wrong? How do I obtain the solution for r2 in Maple?

 

_C1, _C2, _C3 are constant, how to set them constant, to make diff(_C2) = 0 etc

eval(simplify(subs(a=_C1,subs(b=1/(diff(c(t), t)),subs(c=_C2+_C3*exp(-t),eq2)))));

(diff(_C2(t), t)+(diff(_C3(t), t))*(exp(-t))(t)+_C3(t)*(diff((exp(-t))(t), t)))*(-(diff(_C1(t), t))*(diff(diff((c(t))(t), t), t))/(diff((c(t))(t), t))^2+(diff(s(t), t))/(diff((c(t))(t), t)))
a

hi.please see attached file and explain how i remove error

thanks alot

error3.mw

I am trying to integrate solutions to a set of differential equations I have obtained numerically but keep getting this error:

Error, (in solW) invalid input: subs received sol(r), which is not valid for its 1st argument

For simplicity, let's say I am interested in integrating the function W(r), which I obtain from 

sol := dsolve({eqns, ics}, numeric, abserr = 10^(-10), relerr = 10^(-10), range = ymin .. ymax)

I then use

solW := r -> subs(sol(r), W(y))

This gives me W(r) for any r in the range ymin to ymax. But I cannot do anything with this function. For example, 

int(solW(r),r=ymin..ymax) or plot(solW(r),r=ymin..ymax) give the error above. I know that I can plot the solutions using odeplot, but is there something analogous for integrating the solutions? 

Thanks!

Here it is:

 

 

 

 

I'd like to input it as 2-D and solve for x as a function of t.

 

hello guys,

 

i have 4 differential equations with 4 unknown functions and i want to find functions , what is your idea ?

 

diff.mw

 

thank you very much

Dear all,

I have to differential equations that I'd like to linearise, that is all higher order (>1) derivatives (like diff(uu[0],x$2)) and parameters (like beta^2) and the products of any derivatives with the parameters uu[0] and beta are zero (as they are assumed small).

The two equations considered are displayed below:

 

Up to now, I perform a very tedious substitution which is based on looking at the equations above and decide which terms I want to get rid of. Something like this, where K =1:KFBCLin:=simplify(eval(KFBC, [beta^3 = 0, beta^2 = 0,
seq(subs((diff(uu[n], x$3)) = 0),n=0..K),
seq(subs((diff(uu[n], x$2)) = 0),n=0..K),
seq(subs((diff(uu[n], t))*beta = 0),n=0..K),
seq(subs((diff(uu[n], x))^2 = 0),n=0..K),
seq(subs(g*diff(beta, x)*beta = 0),n=0..K),
seq(subs((d^2*diff(uu[n], x,t)*diff(beta,x)=0)),n=0..K),
seq(subs(-2*d*diff(uu[n], x,t)*beta*diff(beta,x)=0),n=0..K),
seq(subs((d^2*diff(uu[n], x$2,t)*beta=0)),n=0..K),
seq(subs((diff(uu[n], x)*uu[n])=0),n=0..K),
seq(subs((diff(uu[n], x)*uu[n]*beta)=0),n=0..K),
seq(subs((diff(uu[n], x)*uu[n]*d)=0),n=0..K),
seq(subs((diff(beta, x)*uu[n])=0),n=0..K),
seq(subs((diff(uu[n], x)*beta)=0),n=0..K)]));As there is a lack of automatisation, this procedure is not very helpful. Life would be easier if there was a command (or the like) that says "get rid of higher order derivatives".Any help is appreciated.Best regards,

Hello, dear experts.
I have a question...
solve the system of differential equations,where one of the initial conditions need to be chosen so thatcondition is metat the end of integration.
The task is not difficult, but I'm having trouble with the syntax.

1.I can't "pull"the desired function from the solution and find its value at a certain point.
I try to do so:
r_ravn:=s->subs(F,r(s));
evalf(r_ravn(s_end));
evalf(r_ravn(0));
but there is no result

2.In this case,instead of"for"it is better to use a while loop, but again the problem arises 1.
Tell me, please,how to implemen my program.

 

restart:
R:=0.3:
theta_min:=Pi/6:
theta_max:=Pi/2:
betta_max:=evalf(Pi/180*80);
p:=2*10^5:

theta0:=s->Pi/3/s_end*s+Pi/6:
r0:=s->R*sin(theta0(s)):
s_end:=evalf(R*(theta_max-theta_min)):

sol1:=solve({sin(betta_max)=c/r0(0)},{c});
const1:=0.1477211630;

betta0:=s->arcsin(const1/r0(s)):
betta:=s->arcsin(r(s)/r0(s)*sin(betta0(s))):
A:=s->cos(betta(s))/cos(betta0(s)):
T1:=s->rT1(s)/r(s):
T2:=s->T1(s)*tan(betta(s))^2:

step:=0.001:
delta:=0.001:
for i from 1 to 3000 do
r_min:=0.3-step:
rT1_n:=p*Pi*r_min^2/2/Pi/sin(theta_min):

sys := diff(rT1(s), s)-A(s)*T2(s)*cos(theta(s)),diff(theta(s), s)-A(s)/T1(s)*(p-T2(s)*sin(theta(s)/r(s))),diff(r(s),s)-A(s)*cos(theta(s)),diff(z(s),s)-A(s)*sin(theta(s));
fcns := {rT1(s),theta(s),r(s), z(s)};
F := dsolve({sys,rT1(0)=rT1_n, theta(0)=theta_min,r(0) = r_min, z(0) = 0}, fcns, numeric,output=listprocedure):
r_ravn:=s->subs(F,r(s)):
if abs(evalf(r_ravn(s_end))-R)=delta then break:
print(r_min):
end if:
end do:

r_ravn:=s->subs(F,r(s));
evalf(r_ravn(s_end));
evalf(r_ravn(0));
plot([r_ravn(s),r(s)],s=0..s_end);

Hi,

I have a system of nonlinear equations in conjuction with boundary conditions, as below:

(all coefficients are constant.)

dsys3 := {a2*(diff(f1(x), x, x))+a3*(diff(f2(x), x, x, x))+a4*(diff(f2(x), x))+a6*(diff(f3(x), x))+a7*f1(x)+a1N*(diff(f3(x), x, x))*(diff(f3(x), x))+a2N*(diff(f3(x), x))*f3(x)+a3N*(diff(f3(x), x))*f3(x) = 0, a8*(diff(f2(x), x, x, x, x))+a9*(diff(f2(x), x, x))+a10*f2(x)+a11*(diff(f1(x), x, x, x))+a12*(diff(f1(x), x))+a13*(diff(f3(x), x, x))+a14*f3(x)+a4N*(f3(x)*f3(x))+a5N*((diff(f3(x), x))*(diff(f3(x), x)))+a6N*(diff(f3(x), x, x))*f3(x) = 0, (diff(f3(x), x, x, x, x))*a16+(diff(f3(x), x, x))*a18+(diff(f3(x), x, x))*a19+(diff(f1(x), x))*a22+(diff(f1(x), x))*a23+(diff(f2(x), x, x))*a24+f2(x)*a25+f2(x)*a26+f3(x)*a27+f3(x)*a29 = 0, f1(0) = 0, f1(1) = 0, f2(0) = 0, f2(1) = 0, f3(0) = 0, f3(1) = 0, ((D@@1)(f2))(0) = 0, ((D@@1)(f2))(1) = 0, ((D@@1)(f3))(0) = 0, ((D@@1)(f3))(1) = 0}:
dsol5 := dsolve(dsys3, 'maxmesh' = 500, abserr = .1, numeric, range = 0 .. 1, output = listprocedure)

but i encounter an error as:

Error, (in dsolve/numeric/bvp/convertsys) unable to convert to an explicit first-order system

what is your suggestion to solve this nonlinear equations?

Thank you.

d2u/dt2-(2*d2u/x2)+d2u/dxdt=0    

initial condition: u(x,0)=1-x, abslute x<1   Ut(x,0)=cos(pix), bslute x<1 

B.C U(-4,t)=U(4,t)=0,   delta x=0.1, delta t=0.025, range 0..4                                      

I want to solve the following differential equation


solve
(y''(x)=(λ*x* y[x])/Sqrt(-1+ x), y(x),x)


But do not know how to actually solve it. Any suggestion?
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