Runge-Kutta Method

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Daniel Diego
Daniel Diego on 21 May 2016
Edited: James Tursa on 23 May 2016

i got 2 equation first one is dVc/dt=ic second one is dIl/dt=-4vc-4il+20 i've been trying everything but nothing worked if someone can help that'd be great.

clc
f=inline('ic','t','ic','il');
g=inline('-4*vc-4*il+20','t','ic','il');
solution_ic=inline('5-(5*exp(-2*t)*(1+2*t))','t');
solution_il=inline('20*t*exp^(-2*t)','t');
h=.1; 
t=0; ic=0; il=0.3839;
hold;
while (t<10)
    k1=h*f(t,ic,il);
    i1=h*g(t,ic,il);
    k2=h*f(t+h/2,ic+k1/2,il+i1/2);
    i2=h*g(t+h/2,ic+k1/2,il+i1/2);
    k3=h*f(t+h/2,ic+k2/2,il+i2/2);
    i3=h*g(t+h/2,ic+k2/2,il+i2/2);
    k4=h*f(t+h,ic+k3,il+i3);
    i4=h*g(t+h,ic+k3,il+i3);
    ic=ic+(1/6)*(k1+2*k2+2*k3+k4);
    il=il+(1/6)*(i1+2*i2+2*i3+i4);
      plot(t,ic,il,'*');
      plot(t,solution_ic(t+h),solution_il(t+h),'bo');
      t=t+h;
  end;
  grid;

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