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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?

eul:=proc(f,h,x0,y0,xn)
  local no_points,x_old,x_new,y_old,y_new,i:
  no_points:=round(evalf((xn-x0)/h)):
  x_old:=x0:
  y_old:=y0:
 
  for i from 1 to no_points do
      x_new:=x_old+h:
      y_new:=y_old+evalf(h*f(x_old,y_old)):
      x_old:=x_new:
      y_old:=y_new:
  od:
  y_new:
end:


Thanks

As it says in the title, I would like to solve the following ODE numerically using forward Euler method, without using the Student Package.

 

(dy(t))/(dt)=t(1-0.3t)-(ty)(1+0.6t)

with initial condition y(0)=1. I want to solve it for up to t=1, and then plot both the solution by Euler's method and the solution by "dsolve" on the same graph so I can compare them.

 

Also, can I make a separate DEplot with t extending to 5?

 

Thanks in advance.

Can someone explain to me, if you can, how the Euler angles on the plot interface work?

 

It looks like Phi is the rotation around z, Theta is the rotation around x, and Psi is around y. I'm trying to use matrices to compute the vector that is pointing towards your face as you're looking at the plot with the given Euler angles.


X := Matrix(3, 3, {(1, 1) = 1, (1, 2) = 0, (1, 3) = 0, (2, 1) = 0, (2, 2) = cos(phi), (2, 3) = sin(phi), (3, 1) = 0, (3, 2) = -sin(phi), (3, 3) = cos(phi)});


Y := Matrix(3, 3, {(1, 1) = cos(theta), (1, 2) = 0, (1, 3) = sin(theta), (2, 1) = 0, (2, 2) = 1, (2, 3) = 0, (3, 1) = -sin(theta), (3, 2) = 0, (3, 3) = cos(theta)});


Z := Matrix(3, 3, {(1, 1) = cos(psi), (1, 2) = sin(psi), (1, 3) = 0, (2, 1) = -sin(psi), (2, 2) = cos(psi), (2, 3) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = 1});

and computing X*Y*Z*e3

 

TIA!

I am a student taking differential equations and I need to implement Euler's method using Maple 17. I have set up a do loop that looks like this:

for i from 1 to n1 do
k:= f(t,v):
v:= v + h*k:
t := t + h:
od:

Where n1 is initialized to 50, f(t,v) := 0.0207v2 -893.58, and h is 0.1. v and t are both initialized as 0.

Hi, I got a doubtI don’tknow how to make the Runge-Kutta’s and Euler’s method. The Runge-Kutta for thesecond and fourth order. I don’t know how to beginning the algoritms, I needsome help. Thanks.

Aqui les dejo La ecuación de la Recta de Euler, calculado desde su inicio hasta la comprobación con el comando EulerLine.

Recta_de_Euler.mw

[I split this off as a separate Question, cleaned up the machine-generated Title, added the Tags, and cleaned out some excessive blank lines.---Carl Love as Moderator]

could anyone help me with my euler plot too!

> with(plots):with(DEtools):

 

Equations & Initial conditions

> de1:=D(x)(t)=a*x(t)-q*x(t)*y(t)-n*x(t)*z(t);

>

I am currently trying to integrate a long string of fractional sine and cos terms with a cos term on the denominator and other exponential multipliers, but all variables and coefficients are real (and I have put this assumption in Maple).

When I integrate them on Maple it is automatically simplifying the result using Euler's rule to give me a complex fraction with a complex numerator and denominator. This is not very helpful as I need to use the result in further calculation,...

I am trying to write out a code to solve for current in a LRC circuit. I have written a code that I think is capable of doing this but keep getting a recursive assignment message in my for loop. I have looked it over about a hundred times and can't see where I have defined a variable in terms of itself. Any help on this would be greatly appreciated. A copy of my code so far is listed below.

> with(plots);
> u := proc (t, Q, dQdt) options operator, arrow; 0.15e-2*cos(omega*t...

How do I look for a 9 digit pi-sequence within decimal places of the EULER e  and find the position of that string.

2,71828182..............314159265..........

      123.....................x

can someone show me screen shot how to do this??

thanks so much

Horst

Hello!

 

I'm currently trying to program Euler's Nummerical Method to solve a second order differential equation, that I've split into two parts: 

f1:=v:

f2:=-(0.006549/0.7038)*v-sin(x/1.03)*9.82

 

In an attempt to solve this equation by using Euler's in Maple, I typed in the following commands: 

 

EulerSystem:=proc (f1,f2,t0,x0,v0,h,n) local t,x,v,i,p;
t[0]:=0; x[0]:=x0; v[0]:=v0;

Hi

So the question is to find complex number W from :

.

but I want the answer in polar form using e (Euler's number).

The question is specific to ask for the complex number W that lying in the first quadrant and having the largest possible real part. I calculated and got :

I am trying to model a multibody system using euler lagrange equation. There are 3 links in the system attached with each other by revolute joints. The first link has one end fixed with the revolute joint.

Length of links= l1,l2,l3

Angle with x axis=Theta1,Theta2,Theta3

Mass of links=m1,m2,m3

Moment of Inertia = M1,M2,M3

I am not able to find the solution of ODE system comprising of 3 ODEs which I get after solving Euler Lagrange Eq for...

I'm using the commands:

RungeKutta(d/dt(y(t))=-y(t),y(0)=1,t=1,submethod=rk4,output=plot,numsteps=10);

Euler(d/dt(y(t))=-y(t),y(0)=1,t=1,output=plot,numsteps=10);

Each of these commands yields its own serperate graph.  How can I plot both on graph to see how the approximations vary?

 

Thanks!

How do you enter h in a Euler's method problem? I need to change h=0.1 to h=0.05

I'm using the 2D input in Maple 14.

So far I have this:

> DE2 := diff(y(t), t) = 3+t-y(t);

> Euler(DE2, y(0) = 1, t = .4);

> Euler(DE2, y(0) = 1, t = .4, output = Error);

> Euler(DE2, y(0) = 1, t = .4, output = information);

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