function w = Euler
%MATLAB routine for visualizing Euler's method
%Created by Winfried Just, department of Mathematics, Ohio University
%Last modified: February 6, 2003
syms t y
disp(' ')
input('Enter the right-hand side of the differential equation. \n');
f = ans
disp(' ')
input('Enter the given solution of the boundary value problem. \n');
g = ans
disp(' ')
input('Enter the value of a. \n');
a = ans
disp(' ')
input('Enter the value of y(a). \n');
ya = ans
disp(' ')
input('Enter the argument b for which you want to find y(b). \n');
b = ans
while 0 < 1
disp(' ')
input('Enter the value of Delta t or Ctrl^C to quit. \n');
dt = ans
y0 = ya;
t0 = a;
hold off
ezplot(g, [a - 0.5, b + 0.5])
hold on
while t0 + 0.0000000000001 < b
t1 = t0 + dt;
y1 = double(subs(f, [t y], [t0 y0])*dt + y0);
x = t0:dt/50:t1;
plot(x, (y1 - y0)*(x - t0)/(t1 - t0) + y0)
t0 = t1;
y0 = y1;
end
error = subs(g, t, b) - y1
end
