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# Fourth order Runge-Kutta ODE solver

This is a simple and direct implementation of fourth order runge-kutta ordinary differential equation solver algorithm. In the main function three use cases are shown.

 ``` 1: 2: 3: 4: 5: 6: 7: 8: 9: 10: 11: 12: 13: 14: 15: 16: 17: 18: 19: 20: 21: 22: 23: 24: 25: 26: 27: 28: 29: 30: 31: 32: 33: 34: 35: 36: 37: 38: 39: 40: 41: ``` ``````open System // -- | ODE, y = e ^ x let mydydx1 x y = exp(x) // -- | ODE, y = x * e ^ 3 * x - 2 * y let mydydx2 x y = x * exp (3.0 * x) - 2.0 * y //-- | ODE, y = r * y let mydydx3 x y = let r = 0.5 r * y // -- | Fourth order runge-kutta algorithm calculations let rungekutta4' x y h f = let k1 = h * f x y let k2 = h * f (x + 0.5 * h) (y + k1 * 0.5) let k3 = h * f (x + 0.5 * h) (y + k2 * 0.5) let k4 = h * f (x + h) (y + k3) y + 1.0/6.0 * (k1 + 2.0 * k2 + 2.0 * k3 + k4) // -- | Fourth order runge-kutta solver let rec rungekutta4 x y h n f xx yy = let y' = rungekutta4' x y h f if (x >= n) then (xx,yy) else rungekutta4 (x+h) y' h n f (List.append xx [x+h]) (List.append yy [y']) // -- | The main entry point. let main() = Console.WriteLine("Welcome to fourth order Runge-Kutta ODE solver!") let v = rungekutta4 0.0 1.0 0.01 1.0 mydydx1 [] [] printfn "%A" ( (snd v).Item ((List.length (snd v)) - 1)) let v = rungekutta4 0.0 0.0 0.01 1.0 mydydx2 [] [] printfn "%A" ( (snd v).Item ((List.length (snd v)) - 1)) let v = rungekutta4 0.0 2.0 0.01 3.0 mydydx3 [] [] printfn "%A" ( (snd v).Item ((List.length (snd v)) - 1)) main() ``````
namespace System
val mydydx1 : x:float -> y:'a -> float

Full name: Script.mydydx1
val x : float
val y : 'a
val exp : value:'T -> 'T (requires member Exp)

Full name: Microsoft.FSharp.Core.Operators.exp
val mydydx2 : x:float -> y:float -> float

Full name: Script.mydydx2
val y : float
val mydydx3 : x:'a -> y:float -> float

Full name: Script.mydydx3
val x : 'a
val r : float
val rungekutta4' : x:float -> y:float -> h:float -> f:(float -> float -> float) -> float

Full name: Script.rungekutta4'
val h : float
val f : (float -> float -> float)
val k1 : float
val k2 : float
val k3 : float
val k4 : float
val rungekutta4 : x:float -> y:float -> h:float -> n:float -> f:(float -> float -> float) -> xx:float list -> yy:float list -> float list * float list

Full name: Script.rungekutta4
val n : float
val xx : float list
val yy : float list
val y' : float
Multiple items
module List

from Microsoft.FSharp.Collections

--------------------
type List<'T> =
| ( [] )
| ( :: ) of Head: 'T * Tail: 'T list
interface IEnumerable
interface IEnumerable<'T>
member IsEmpty : bool
member Item : index:int -> 'T with get
member Length : int
member Tail : 'T list
static member Cons : head:'T * tail:'T list -> 'T list
static member Empty : 'T list

Full name: Microsoft.FSharp.Collections.List<_>
val append : list1:'T list -> list2:'T list -> 'T list

Full name: Microsoft.FSharp.Collections.List.append
val main : unit -> unit

Full name: Script.main
type Console =
static member BackgroundColor : ConsoleColor with get, set
static member Beep : unit -> unit + 1 overload
static member BufferHeight : int with get, set
static member BufferWidth : int with get, set
static member CapsLock : bool
static member Clear : unit -> unit
static member CursorLeft : int with get, set
static member CursorSize : int with get, set
static member CursorTop : int with get, set
static member CursorVisible : bool with get, set
...

Full name: System.Console
Console.WriteLine() : unit
Console.WriteLine(value: string) : unit
Console.WriteLine(value: obj) : unit
Console.WriteLine(value: uint64) : unit
Console.WriteLine(value: int64) : unit
Console.WriteLine(value: uint32) : unit
Console.WriteLine(value: int) : unit
Console.WriteLine(value: float32) : unit
Console.WriteLine(value: float) : unit
Console.WriteLine(value: decimal) : unit
val v : float list * float list
val printfn : format:Printf.TextWriterFormat<'T> -> 'T

Full name: Microsoft.FSharp.Core.ExtraTopLevelOperators.printfn
val snd : tuple:('T1 * 'T2) -> 'T2

Full name: Microsoft.FSharp.Core.Operators.snd
val length : list:'T list -> int

Full name: Microsoft.FSharp.Collections.List.length