Re: Octave code for y'''=0 ODE

[Tatsuro MATSUOKA]

----- Original Message -----

> From: deepus 
> To: help-octave
> Cc: 
> Date: 2015/7/28, Tue 13:22
> Subject: Octave code for y'''=0 ODE
> 
> Find the particular solution of
> 
> y'''=0
> ​​
> given that:
> 
> y(0)=3, y'(1)=4, y''(2)=6
> 
> How can I write the Octave code for  solve the above equation?
> Please help me...
> 
> 


In general, to solve higher order ordinal differential equation,
the problem modified to first order simultaneous differential equations.

y1'=y2

y2'=y3
y3'=0
y1(0)=3
y2(1)=4
y3(2)=6

However
The manual of lsode states:


The set of differential equations to solve is
dx
-- = f (x, t)
dt 
with
x(t_0) = x_0 
The solution is returned in the matrix x, with each row corresponding to an 
element of the vector t. The first element of t should be t_0 and should 
correspond to the initial state of the system x_0, so that the first row of the 
output is x_0.

is not case of 
"The first element of t should be t_0 and should correspond to the initial 
state of the system x_0, so that the first row of the output is x_0."

The above special case
y3=const, y2 changes linearly to t.

Thus
y1(0)=3
y2(0)=-2
y3(0)=6

gives correct results.
Thus

f=@(y,t)[y(2);y(3);0];

t=0:1:10;
y_0=[3 -2 6];
y=lsode(f,y_0,t);



Then
>> [t' y]
ans =

     0.00000     3.00000    -2.00000     6.00000
     1.00000     4.00000     4.00000     6.00000
     2.00000    11.00000    10.00000     6.00000
     3.00000    24.00000    16.00000     6.00000
     4.00000    43.00000    22.00000     6.00000
     5.00000    68.00000    28.00000     6.00000
     6.00000    99.00000    34.00000     6.00000
     7.00000   136.00000    40.00000     6.00000
     8.00000   179.00000    46.00000     6.00000
     9.00000   228.00000    52.00000     6.00000
    10.00000   283.00000    58.00000     6.00000


But the above is rare case. 

However I do not know general way to set the initial dependent variables depend 
on different t_0 values.

Perhaps much experts for ode will give solutions.

Tatsuro