Thread Subject:

Adams-Bashforth-Moulton method

Hi, I have a huge problem. I have to write a script that solve differential equation like this
2000y"=98(1+y')^2{t(t-1)+2}
using Adams-Bashforth-Moulton method and then compare results using ode45. I wrote a function

>function dy = belka(t,y)
>% funkcja w której zapisali?my równanie różniczkowe
>dy=zeros(2,1) ;
>dy(1)=y(2);
>dy(2)=(9.8*10/2000)*(1+y(2))^2*{t.*(t-1)+2};
>end

And I have a function

>function [ t, y ] = ode_abm( f, tspan, y0, N, KC, varargin )
>%UNTITLED Summary of this function goes here
>% Detailed explanation goes here
>if nargin<5, KC=1; end
>if nargin<4 | N<=0. N=100; end
>y0=y0(:)';
>h=(tspan(2)-tspan(1))/N;
>tspan0=tspan(1)+[0 3]*h;
>[t, y]=rk4(f, tspan0, y0, 3, varargin{:});
>t=[t(1:3)' t(4):h:tspan(2)]';
>for k=1:4, F(k,:)=feval(f, t(k), y(k,:), varargin{:}); end
>p=y(4,:); c=y(4,:); KC22=KC*251/270; KC12=KC*19/270;
>h24=h/24; h241=h24*[1 -5 19 9]; h249=h24*[-9 37 -59 55];
>for k=4:N
> p1=y(k,:)+h249*F;
> m1=pk1+KC22*(c-p);
> c1=y(k,:)+h241*[F(2:4,:); feval(f,t(k+1), m1, varargin{:})];
> y(k+1,:)=c1-KC12*(c1-p1);
> p=p1; c=c1;
> F=[F(2:4,:);feval(f,t(k+1),y(k+1,:), varargin{:})];
>end
>end
 
It has inside function rk4, so

function [ t, y ] = rk4( f, tspan, y0, N, varargin )
%UNTITLED8 Summary of this function goes here
% Detailed explanation goes here
if nargin<4 | N<=0, N=100; end
if nargin<3, y0=0; end
y(1,:)=y0(:)';
h=(tspan(2)-tspan(1))/N; t=tspan(1)+[0;N]'*h;
for k=1:N
    f1=h.*feval(f,t(k),y(k,:),varargin{:}); f1=f1(:)';
    f2=h.*feval(f,t(k)+h/2,y(k,:)+f1/2,varargin{:}); f2 = f2(:)';
    f3=h.*feval(f,t(k)+h/2,y(k,:)+f2/2,varargin{:}); f3 = f3(:)';
    f4=h.*feval(f,t(k)+h,y(k,:)+f3,varargin{:}); f4 = f4(:)';
    y(k+1,:)=y(k,:)+(f1+2.*(f2+f3)+f4)/6;
end
 
But i doesn't work. Matlab says

>> [t, y]=ode_abm(@belka, [0 2], [0 0], 100, 1)
??? Undefined function or method 'mtimes' for input arguments of
type 'cell'.

Error in ==> belka at 5
dy(2)=(9.8*10/2000)*(1+y(2))^2*{t.*(t-1)+2};

Error in ==> rk4 at 9
    f1=h.*feval(f,t(k),y(k,:),varargin{:}); f1=f1(:)';

Error in ==> ode_abm at 9
[t, y]=rk4(f, tspan0, y0, 3, varargin{:});

What is wrong? Could anyone help me? That means a lot for me. I am really bad it Matlab, so please- give me simple explanation ;)

"Emilia Przybysz" <emilia.przybysz0909@gmail.com> wrote in message
news:46eeeba3-e22b-4db4-8726-6cb19b69a47d@googlegroups.com...
> Hi, I have a huge problem. I have to write a script that solve
> differential equation like this
> 2000y"=98(1+y')^2{t(t-1)+2}
> using Adams-Bashforth-Moulton method and then compare results using ode45.
> I wrote a function
>
>>function dy = belka(t,y)
>>% funkcja w ktrej zapisali?my rwnanie rniczkowe
>>dy=zeros(2,1) ;
>>dy(1)=y(2);
>>dy(2)=(9.8*10/2000)*(1+y(2))^2*{t.*(t-1)+2};

The section:

{t.*(t-1)+2}

creates a cell array. MATLAB doesn't know how to multiply the previous term
in the definition for dy(2):

(9.8*10/2000)*(1+y(2))^2

and a cell array -- it's not defined. Use parentheses instead of curly
braces if all you want to do is group together the expression representing
"t times t-1, plus 2", just like you used parentheses to group the
expression "9.8 times 10 divided by 2000."

*snip*

>>[t, y]=rk4(f, tspan0, y0, 3, varargin{:});

Here and in the similar function evaluation calls later in your code curly
braces ARE needed, as you're working with the cell array VARARGIN.

*snip*

--
Steve Lord
slord@mathworks.com
To contact Technical Support use the Contact Us link on
http://www.mathworks.com

Thanks :)
I changed curly brases to parentheses and that's ok- I checked with ode113.
But I still don't know what should I do with your second piece of advice. Where should I put curly brases? How to change this part
>>[t, y]=rk4(f, tspan0, y0, 3, varargin{:});

Thanks :)
I changed curly braces to parentheses and that's ok- I checked with ode113.
But I still don't know what should I do with your second piece of advice. Where should I put curly braces? How to change this part
>>[t, y]=rk4(f, tspan0, y0, 3, varargin{:});

On 05.02.13 19:52, Emilia Przybysz wrote:
> Thanks :)
> I changed curly braces to parentheses and that's ok- I checked with ode113.
> But I still don't know what should I do with your second piece of advice. Where should I put curly braces? How to change this part
>>>[t, y]=rk4(f, tspan0, y0, 3, varargin{:});
>

Don't change it. Steven just said you should not change all curly braces
you have anywhere, since in this place, they are exactly what you need.


HTH,
Christopher