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according to my previous question

I wrote the following code. at first, the code solve the equation for f and when it slves that, I want to solve Theta in such a way that use the values of f in previous calculation. I use the command 'known' but i couldnt find thesolution

I would be most grateful if you could help me in this problem

Thanks for your attentions in advance

restart; # Notice that Restart (capital R) has no effect (to catch that use semicolon, not colon)

Q:=proc(pp2) local res,F0,F1,F2;
if not type(pp2,numeric) then return 'procname(_passed)' end if:
end proc;


plots:-odeplot(res2,[seq([x,diff(f(x),[x$i])],i=0..2)],0..2); #This plots from and past 0.1*c


QT:=proc(pp3) local res3,theta0,theta1;
if not type(pp3,numeric) then return 'procname(_passed)' end if:
end proc;



Hi. I am trying to identify mode shapes (phi(x)) and natural frequencies  of non-uniform euler-bernoulli beam. There are number of numerical methods to solve ODE with certain boundary conditions (i.e. Runge Kutta method). Problem is that I am newbie here. I am interested in particularly first vibration mode and its frequency. Is there anyone acquainted with it and would be able to help me?

I was given that solitary initial state to see how it will deform as time goes on. am struggling to get my code so that I can get video frames. please help on how I can generate my code


uo(x)= a0x2(1-x)2 for x (less than or equal to) x (less than or equal) 1

u0(x)    = 0 for x > 1

the video clips will be representing the function u(*,t) :x to u(x,t)

for a sequence of choices of t such as t=0; t=0,5...t=3


i am using maple to solve a system of ordinary differential equations , 3 unknows (x,y, x ), and 3 equations (dx/dt,dy/dt,dz/dt)

there is one known variable denpendent on x and z

# code begins here

if x(t) <= z(t) then Q(t) := 8 end if;

if x(t) > z(t) then Q(t) := 10 end if;


eq1 := diff(x(t), t) = 3*x(t)-1;

eq2 := diff(y(t), t) = y(t)+Q(t);

eq3 := diff(z(t), t) = z(t);

eqs := {eq1, eq2, eq3};


# code ends here


above i put the system of ODEs, the code maybe illegal in maple, but i wrote in this way to make it clear.

Q is dependent on x and z.


in the past, when i was trying to solve ODEs, normally, eqs contains with only x,y,z as unknowns. but in this eqs, clearly, Q is included as an unknown. 


i've tried to use piecewise function to express Q(t), but failed.


how could i solve a system like this? thanks 



Here is the ODE:


dsolve((y(x)^2-x)*(D(y))(x)+x^2-y(x) = 0, {y(x)})


And the Maple 18 returns a very complex result.

But as we know,the more elegant result should be this:


How can I get this simple result with Maple?

I'm working on coupled differential equation.
The first system is : 

And the second one : 
q2''(t)+e(q22-1)q2'(t)+q2(t) = y2"+f(P) q1(t-tau)

This is a parametric system, f(P) and tau(P) are given function of the parameters P.
e is a constant

I have solved the first system with dsolve (using numeric option).
But when I try to solve the second one (with dsolve, numeric, setting P as a parameter), maple returns an error : 

"Error, (in dsolve/numeric/process_input) input system must be an ODE system, got independent variables {t, t-1}"

I think Maple doesn't like " q1(t-tau)".
I have tried to create a new function q where :
But Maple returns the same error.

How can I fix it ?

Thanks for reading

EDIT : I have read there is no function in maple that solve delay differential equation.
But this is not a true DDE because q2 has no effect on q1
So I hope there is a way to "fool" maple and still use dsolve.

EDIT 2 :
I have found how to make it works.
I was using dsolve with the option compile (which increase (a lot) the efficiency of computation).
I delete this option and that's working.
Nevertheless, without the option compile, the computation is very very slow.
MapleHelp recommands to combine the 2 systems for more efficiency. But, when I combine, maple return the previous error.
How can I make it quicker ?

Here is the code : 

ode := diff(sqrt(U(t)), t) = sqrt(U__0)-sqrt(U(t))

ics := U(0) = 0

dsolve({ics, ode})


And the result maple returns is U(t)=0 !



im solving 6 ODE which is the equations are unsteady with boundary conditions.. the program can be run when A=0 but when A=0.2 or others value .. its cannot be run... A means for unsteadiness... before this i solve for steady equations.. this is first time i solve for unsteady using maple.. anyone know where i am wrong??? thanks for helping :)


restart; with(plots); n := 2; Ec := 2.0; Pr := .72; N := .2; M := .1; l := 1; Nr := 1; y := 1; blt := 2.5; B := .1; a1 := 1; rho := .5

Eq1 := diff(f(eta), eta, eta, eta)+f(eta)*(diff(f(eta), eta, eta))-(diff(f(eta), eta))^2+l*B*H(eta)*(F(eta)-(diff(f(eta), eta)))-M*(diff(f(eta), eta))-A*(diff(f(eta), eta)+.5*eta*(diff(f(eta), eta, eta))) = 0;

diff(diff(diff(f(eta), eta), eta), eta)+f(eta)*(diff(diff(f(eta), eta), eta))-(diff(f(eta), eta))^2+.1*H(eta)*(F(eta)-(diff(f(eta), eta)))-.1*(diff(f(eta), eta))-A*(diff(f(eta), eta)+.5*eta*(diff(diff(f(eta), eta), eta))) = 0


Eq2 := A*(F(eta)+.5*eta*(diff(F(eta), eta)))+G(eta)*(diff(F(eta), eta))+F(eta)^2+B*(F(eta)-(diff(f(eta), eta))) = 0;

A*(F(eta)+.5*eta*(diff(F(eta), eta)))+G(eta)*(diff(F(eta), eta))+F(eta)^2+.1*F(eta)-.1*(diff(f(eta), eta)) = 0


Eq3 := .5*A*(G(eta)+.5*eta*(diff(G(eta), eta)))+G(eta)*(diff(G(eta), eta))+B*(f(eta)+G(eta)) = 0;

.5*A*(G(eta)+.5*eta*(diff(G(eta), eta)))+G(eta)*(diff(G(eta), eta))+.1*f(eta)+.1*G(eta) = 0


Eq4 := G(eta)*(diff(H(eta), eta))+H(eta)*(diff(G(eta), eta))+F(eta)*H(eta) = 0;

G(eta)*(diff(H(eta), eta))+H(eta)*(diff(G(eta), eta))+F(eta)*H(eta) = 0


Eq5 := (1+Nr)*(diff(theta(eta), eta, eta))+Pr*((diff(theta(eta), eta))*f(eta)-2*(diff(f(eta), eta))*theta(eta))+N*Pr*a1*(theta1(eta)-theta(eta))/rho+N*Pr*Ec*B*(F(eta)-(diff(f(eta), eta)))^2/rho+Pr*Ec*(diff(f(eta), eta))^2-.5*A*Pr*(4*theta(eta)+eta*(diff(theta(eta), eta))) = 0;

2*(diff(diff(theta(eta), eta), eta))+.72*(diff(theta(eta), eta))*f(eta)-1.44*(diff(f(eta), eta))*theta(eta)+.2880000000*theta1(eta)-.2880000000*theta(eta)+0.5760000000e-1*(F(eta)-(diff(f(eta), eta)))^2+1.440*(diff(f(eta), eta))^2-.360*A*(4*theta(eta)+eta*(diff(theta(eta), eta))) = 0


Eq6 := 2*F(eta)*theta1(eta)+G(eta)*(diff(theta1(eta), eta))+a1*y*(theta1(eta)-theta(eta))+.5*A*(4*theta1(eta)+eta*(diff(theta1(eta), eta))) = 0;

2*F(eta)*theta1(eta)+G(eta)*(diff(theta1(eta), eta))+theta1(eta)-theta(eta)+.5*A*(4*theta1(eta)+eta*(diff(theta1(eta), eta))) = 0


bcs1 := f(0) = 0, (D(f))(0) = 1, (D(f))(blt) = 0, F(blt) = 0, G(blt) = -f(blt), H(blt) = n, theta(0) = 1, theta(blt) = 0, theta1(blt) = 0;

f(0) = 0, (D(f))(0) = 1, (D(f))(2.5) = 0, F(2.5) = 0, G(2.5) = -f(2.5), H(2.5) = 2, theta(0) = 1, theta(2.5) = 0, theta1(2.5) = 0


L := [0., .2, .5];

[0., .2, .5]


for k to 3 do R := dsolve(eval({Eq1, Eq2, Eq3, Eq4, Eq5, Eq6, bcs1}, A = L[k]), [f(eta), F(eta), G(eta), H(eta), theta(eta), theta1(eta)], numeric, output = listprocedure); Y || k := rhs(R[3]); YP || k := rhs(R[5]); YR || k := rhs(R[6]); YQ || k := rhs(R[7]); YA || k := rhs(R[9]); YB || k := rhs(R[8]) end do

Error, (in dsolve/numeric/bvp) initial Newton iteration is not converging


P1 := plot([Y || (1 .. 3)], 0 .. 10, labels = [eta, (D(f))(eta)])

P2 := plot([YP || (1 .. 3)], 0 .. 10, labels = [eta, F(eta)])

plots:-display([P1, P2])

Error, (in plots:-display) expecting plot structures but received: [P1, P2]






i follow the code newton raphson for solve system nonlinear ODE in maple,every body have code for it?


When I run two times my code, the results change.

Have you any idea, why???



Hi , everyone who love Maple and dsolve command, 

my ODE is :

sys_ode := diff(d11(m), m) = -(3*sin(m)^2-1)*d31(m)/a^(3/2)+(-3*cos(m)*sin(m)/a^(3/2))*d41(m), diff(d21(m), m) = (-3*cos(m)*sin(m)/a^(3/2))*d31(m)-(3*cos(m)^2-1)*d41(m)/a^(3/2), diff(d31(m), m) = -a^(3/2)*d11(m), diff(d41(m), m) = -a^(3/2)*d21(m)

using " dsolve([sys_ode]) " command could get the solution easily, and the solution contains "I" (imaginary domain).

However, when we substitute the solution into the ODE "sys_ode", find not correct !

we use the following command to check the solution :

 simplify(  -diff(d11(m), m) -(3*sin(m)^2-1)*d31(m)/a^(3/2)+(-3*cos(m)*sin(m)/a^(3/2))*d41(m)  )

the upper expression is supposed to be zero, but not ! Is it a bug in Maple dsolve ?

Hi, I have a homework to do that I am strugling with:

write a procedure which uses euler's method to solve a given initial value problem.
the imput should be the differential equation and the initial value.
using this programme find y(1) if dy/dx= x^2*y^3 and y(0)=1, and use maple dsolve command to check the solution.

That is what I have managed to do, but somehow it is not working correctelly, can somebody help please?

  local no_points,x_old,x_new,y_old,y_new,i:
  for i from 1 to no_points do



I have numerically solved a system of ODEs and plotted the graphs of a[j](t) for each j=0..21.

It was clear from the picture that each a[j] has a unique zero. Is there a maple command to

locate these zeroes?


 I have the following ODEs

# continuity condition  

the value of c is unknown which must be obtained via D(g(c)):=1;

 How can I solve it?

Thanks for your attentions in advance


im solving 4 ODe with boundary conditions.. i got this error Error, (in dsolve/numeric/bvp/convertsys) too few boundary conditions: expected 8, got 7

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