human
Runge | A sample differential equation " dy / dx ▁ = ▁ ( x ▁ - ▁ y ) /2".
Finds value of y for a given x using step size h and initial value y0 at x0 ..
Count number of iterations using step size or step height h.
Iterate for number of iterations.
Apply Runge Kutta Formulas to find next value of y.
Update next value of y.
Update next value of x.
Driver Code"
Solution in Python:
assistant
#Here is code to runge and the other steps required.
 def dydx ( x , y ) :
	return ( x + y - 2 ) ;
def rungeKutta ( x0 , y0 , x , h ) :
	n = round ( ( x - x0 ) / h ) ;
	y = y0 ;
	for i in range ( 1 , n + 1 ) :
		k1 = h * dydx ( x0 , y ) ;
		k2 = h * dydx ( x0 + 0.5 * h , y + 0.5 * k1 ) ;
		y = y + ( 1.0 / 6.0 ) * ( k1 + 2 * k2 ) ;
		x0 = x0 + h ;
	return y ;
if __name__ == " _ _ main _ _ " :
	x0 = 0 ; y = 1 ;
	x = 2 ; h = 0.2 ;
	print ( " y ( x ) ▁ = " , rungeKutta ( x0 , y , x , h ) ) ;