***home work 4***
DECLARE FUNCTION f! (x!, y!)
CLS
PRINT "The interval is [a,b]"
INPUT "Enter a,b:", a, b
INPUT "Enter y(a):", ya
DIM a(200), s(200), value(200), k1(200), k2(200), k3(200), k4(200)
'                     ******Euler's method*******
n = 1
value(1) = ya + f(a, ya)
WHILE ABS(value(n - 1) - value(n)) > .0001
 n = n + 1
 s(0) = ya
 d = (b - a) / n
 a(0) = a
 FOR i = 1 TO n
  a(i) = i * (1 / n)
 NEXT
 FOR i = 1 TO n
  s(i) = s(i - 1) + d * f(a(i - 1), s(i - 1))
 NEXT
 value(n) = s(n)
WEND
PRINT "Euler's method: y("; b; ")="; value(n), "n="; n

'                      *******Rungkutta of order 2*********
n = 1
value(1) = 1
WHILE ABS(value(n - 1) - value(n)) > .0001
 n = n + 1
 s(0) = ya
 d = (b - a) / n
 a(0) = a
 FOR i = 1 TO n
  a(i) = i * (1 / n)
 NEXT

 FOR i = 1 TO n
  k1(i) = d * f(a(i - 1), s(i - 1))
  k2(i) = d * f(a(i - 1) + d, s(i - 1) + k1(i))
  s(i) = s(i - 1) + .5 * (k1(i) + k2(i))
 NEXT
 value(n) = s(n)
WEND
PRINT "Rungkutta of order 2: y("; b; ")="; value(n), "n="; n
'                      *******Rungkutta of order 4*********
n = 1
value(1) = 1
WHILE ABS(value(n - 1) - value(n)) > .0001
 n = n + 1
 s(0) = ya
 d = (b - a) / n
 a(0) = a
 FOR i = 1 TO n
  a(i) = i * (1 / n)
 NEXT

 FOR i = 1 TO n
  k1(i) = d * f(a(i - 1), s(i - 1))
  k2(i) = d * f(a(i - 1) + d / 2, s(i - 1) + k1(i) / 2)
  k3(i) = d * f(a(i - 1) + d / 2, s(i - 1) + k2(i) / 2)
  k4(i) = d * f(a(i - 1) + d, s(i - 1) + k3(i))
  s(i) = s(i - 1) + (1 / 6) * (k1(i) + 2 * k2(i) + 2 * k3(i) + k4(i))
 NEXT
 value(n) = s(n)
WEND
PRINT "Rungkutta of order 4: y("; b; ")="; value(n), "n="; n
PRINT "for the last method we have:"
PRINT "  k1", "  k2", "  k3", "  k4", " Y"
FOR i = 1 TO n
 PRINT k1(i); k2(i); k3(i); k4(i); s(i)
NEXT

FUNCTION f (x, y)
 f = .1 * (x ^ 2 + y ^ 2)
END FUNCTION