can you please tell me how to implement 4th order RUNGE KUTTA METHOD for more that 3 coupled equations in MATLAB.

regards

faiz

If you have a version for a vector valued ODE for one dimension, you have it for all dimensions. Something like this (syntax may have easily corrected errors, this works under scilab, which is close, but not idential to matlab)

``````function [t, y] = RK4(odefunc, y0, t0, tf, N)
T = tf-t0;
h=T/N;
time=t0;
state=y0;
t = zeros(N+1);
y = zeros(N+1,length(y0));
t(1) = t0;
y(1,:) = y0;

for i=2:N+1
k1 = odefunc(time        , state           );
k2 = odefunc(time + 0.5*h, state + 0.5*h*k1);
k3 = odefunc(time + 0.5*h, state + 0.5*h*k2);
k4 = odefunc(time +     h, state +     h*k3);
state = state + (h/6)*(k1+2*k2+2*k3+k4);
time = time + h;
t(i) = time;
y(i,:) = state;
end
endfunction

function doty = lorenz(t, y, params)
a=params(1); b=params(2); c=params(3);
doty = [ a * ( y(2) - y(1) )
-b * y(1) + y(1) * y(3)
-c * y(1) - b * y(3) ]'
endfunction

function doty=odefunc(t,y)
doty = lorenz(t,y,[0.5, 0.66, 1.4])
endfunction

[T,Y] = RK4(odefunc, [-1.2 0.2 0.8], 0, 10, 400)
``````

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