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Task/Runge-Kutta-method/FutureBasic/runge-kutta-method.futurebasic

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+include "ConsoleWindow"
+
+def tab 9
+
+local fn dydx( x as double, y as double ) as double
+end fn = x * sqr(y)
+
+local fn exactY( x as long ) as double
+end fn = ( x ^2 + 4 ) ^2 / 16
+
+dim as long i
+dim as double h, k1, k2, k3, k4, x, y, result
+
+h = 0.1
+y = 1
+for i = 0 to 100
+x = i * h
+if x == int(x)
+result = fn exactY( x )
+print "y("; mid$( str$(x), 2, len(str$(x) )); ") = "; y, "Error = "; result - y
+end if
+
+k1 = h * fn dydx( x, y )
+k2 = h * fn dydx( x + h / 2, y + k1 / 2 )
+k3 = h * fn dydx( x + h / 2, y + k2 / 2 )
+k4 = h * fn dydx( x + h,     y + k3     )
+
+y = y + 1 / 6 * ( k1 + 2 * k2 + 2 * k3 + k4 )
+next