kutta.m

%runge kutta
%dc/dt = -lambda*c     c(t = 0) =c0 

%assume lambda = 1

clc
close all
clear all
%global lambda =1;
lambda =1;
x0 = 1;
t0 = 0;
h = 2; %h is my dt
i = 1;
n = 100;
x(i) = x0;
while i<=n
  k1 = h*f1(t0,x0);
  k2 = h*f1(t0+h/2,x0+k1/2);
  k3 = h*f1(t0+h/2,x0+k2/2);
  k4 = h*f1(t0+h,x0+k3);
  km = (k1+2*k2+2*k3+k4)/6;
  t1 = t0 + h;
  x1 = x0 + km;
  i = i + 1;
  x(i) = x1;
  t(i) = t1;
  x0 = x1;
  t0 = t1;
end

plot(t,x)
min=0;
max=60;
t2=linspace(min,max,1000);
th=exp(-t2);
hold on
plot(t2,th,'r')
grid off