-- Euler's Method
-- Steve Kifowit
-- June 16, 2009

-- User input
function f(x,y)
   return x*y^2
end

x0 = 0
y0 = 1
Xend = 1
steps = 20
-- No user input required beyond this point, --
-- unless you want to edit the format strings --

h = ( Xend - x0 ) / steps
print("Starting values:")
form1 = "When x = %.6f,   y = %.6f"
io.write( string.format( form1, x0, y0 ), "\n"  )
file = io.open("euler.dat", "w+")
file:write( x0, ", ", y0, "\n" )
for i = 1, steps do
   y0 = y0 + h * f(x0,y0)
   x0 = x0 + h
   file:write( x0, ", ", y0, "\n" )
end
file:close()
print("\nEnding values:")
form2 = "When x = %.6f,   y is approximately %.6f"
io.write( string.format( form2, x0, y0 ), "\n" )
print("\nData from individual steps written to euler.dat")