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Topic: solving via runge-kutta fourth order equation
Replies: 6   Last Post: Jun 20, 2013 9:38 AM

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Torsten

Posts: 1,440
Registered: 11/8/10
Re: solving via runge-kutta fourth order equation
Posted: Jun 20, 2013 6:22 AM
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"Alex" wrote in message <kpsk71$bj1$1@newscl01ah.mathworks.com>...
> "Alex" wrote in message <kpsfh2$rcl$1@newscl01ah.mathworks.com>...
> > "Steven_Lord" <slord@mathworks.com> wrote in message <kpsemn$p3m$1@newscl01ah.mathworks.com>...
> > >
> > >
> > > "Alex " <damdamrgf@yahoo.com> wrote in message
> > > news:kpsd49$km8$1@newscl01ah.mathworks.com...

> > > > Hi there,
> > > >
> > > > I am quite new to matlab and have one question regarding solving odf using
> > > > Runge-kutta fourth order.
> > > >
> > > > I solved it in excel, however looking forward to implement it into matlab
> > > > for better performance.
> > > >
> > > > so i have to solve this equation :
> > > >
> > > > d(ln(Q))/dt=g(Q)*(P/Q-1) ;

> > >
> > > Let Y = log(Q). Thus:
> > >
> > > dY/dt = g(exp(Y))*(P/(exp(Y)-1))
> > >
> > > This is in the form expected by the ODE solvers included in MATLAB. Try
> > > ODE45 first, and if that doesn't work because the problem is too stiff
> > > switch to one of the stiffer solvers. The documentation includes a table
> > > describing which solvers are stiff and which are nonstiff.
> > >

> > > > by solving via runge-kutta it should looks like this:
> > > > ln(Q) in step n+1= ln(Q) at step n + 1/6*h*(s1+2s2+ss3+s4) ;
> > > >
> > > > where Q, and P are know values let say:

> > >
> > > Wait, what? What EXACTLY are you trying to solve for if you already know Q
> > > and P? You're already done, aren't you?
> > >
> > > --
> > > Steve Lord
> > > slord@mathworks.com
> > > To contact Technical Support use the Contact Us link on
> > > http://www.mathworks.com

> >
> > I have just first value of Q as an initial condition that should be used with runge-kutta 4-th order scheme.
> >
> > so ln(Q) in step n+1 (we are searchig for it) = ln(Q) at step n (the initial condition when n=1) + 1/6*h*(s1+2s2+ss3+s4) ;

>
>
> i found some code tthat i could used in my computation. however i have still some problems with input parameters, if someone can help me that would be great. thanks!!!
>
> %so i defined a function as :
> function dxdt = dlogq1(x,P,c1,c2,c3)
>
> %x = log(Q);
> g = c1+c2*x+c3*x^2; % ln(g(Q))= c1+c2*ln(Q)+c3*ln((Q))^2
>
> dxdt = g*((P/exp(x))-1); % d(ln(Q))/dt=g(Q)*(P/Q-1) ;
> end
>
> %main program:
> h=1; % step size
>
> c1=-3.87;
> c2=1.64;
> c3=-0.16;
>
> P=-0.002666;
> dt=1;
> t = 0:h:3; % Calculates upto x(3)
>
> x(1) = log(0.0505); % initial condition
> t = zeros(1,length(t));
>
> for i=1:(length(t)-1) % calculation loop
> k_1 = dlogq1(t(i),x(i));
> k_2 = dlogq1(t(i)+0.5*h,x(i)+0.5*h*k_1);
> k_3 = dlogq1((t(i)+0.5*h),(x(i)+0.5*h*k_2));
> k_4 = dlogq1((t(i)+h),(x(i)+k_3*h));
>
> x(i+1) = x(i) + (1/6)*(k_1+2*k_2+2*k_3+k_4)*h; % main equation
> end
>
> thanks al.


If your function dlogq1 has parameter list
function dxdt = dlogq1(x,P,c1,c2,c3),
you will have to call it with this parameter list.
Thus
for i=1:(length(t)-1) % calculation loop
k_1 = dlogq1(t(i),x(i),c1,c2,c3);
k_2 = dlogq1(t(i)+0.5*h,x(i)+0.5*h*k_1,c1,c2,c3);
k_3 = dlogq1(t(i)+0.5*h,x(i)+0.5*h*k_2,c1,c2,c3);
k_4 = dlogq1(t(i)+h,x(i)+k_3*h,c1,c2,c3);

x(i+1) = x(i) + (1/6)*(k_1+2*k_2+2*k_3+k_4)*h; % main equation
end

Best wishes
Torsten.



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