[Solve a differential equation using 4th order Runge kutta method] An algorithm to solve a Differential equation given the points of x and initial value of y #swift #differential_equations

runge_kutta_4th_order_method.swift

// Solving a differential equation using 4th order runge kutta method


///ALL VARIABLES ARE TO BE IN DOUBLE
/// note the given values are an example. you can replace your own values if you want

let xes :[Double] = [0.0,0.1] // you must input the xn values you want to calculate for

var yn = 1.0 // initial value of y (y0)

let h = 0.1 // the value by which x increments in each step




var xn = xes[0]

func dE(_ x : Double,_ y :  Double) -> Double
{
    return (3 * x) + (y / 2) // replace this with the given f(x,y)
}
func k1() -> Double
{
    return h * (dE(xn, yn))
}

func k2() -> Double
{
    return h * (dE(xn + (h / 2), yn + (k1() / 2 )))
}
func k3() -> Double
{
    return h * (dE(xn + (h / 2), yn + (k2() / 2)))
}
func k4() -> Double
{
    return h * (dE(xn + (h / 2), yn + k3()))
}
func ynext() -> Double
{
    let K1 = k1()
    let K2 = k2()
    let K3 = k3()
    let K4 = k4()
    return yn + ((K1 + (2 * (K2 + K3)) + K4) / 6)
}

for i in 0 ..< xes.count
{
    xn = xes[i]
    print("x\(i) = \(xn)")
    print("k1 = \(k1())")
    print("k2 = \(k2())")
    print("k3 = \(k3())")
    print("k4 = \(k4())")
    yn = ynext()
    print("y\(i + 1) = \(yn)\n")
    
 }
 // code will print the value of yn+1 at the given xn and yn values