A simple example of publishing reports
Contents
The Euler approximation of the differential equation on [0,2]:
Define the grid size, interval's partition, and the initial value
h=0.1;
x=0:h:2;
clear y;
y(1)=1;
Define the function
f=inline('3*exp(-4*x)-2*y');
Compute the Euler approximation
size(x);
for i=1:20 y(i+1)=y(i)+h*f(x(i),y(i));end
The exact solution
Y_exact=2.5*exp(-2*x)-1.5*exp(-4*x);
The differences between exact and approximate solutions
error = abs(Y_exact-y)'
error =
0
0.0587
0.0793
0.0794
0.0696
0.0560
0.0418
0.0289
0.0180
0.0092
0.0025
0.0024
0.0058
0.0080
0.0093
0.0099
0.0100
0.0097
0.0092
0.0086
0.0079
Plot of the exact and approximate (dashed curve) solutions
plot(x,y,'--',x,Y_exact)