Data commit

Task/Runge-Kutta-method/Racket/runge-kutta-method-1.rkt

@@ -0,0 +1,8 @@
+(define (RK4 F δt)
+  (λ (t y)
+    (define δy1 (* δt (F t y)))
+    (define δy2 (* δt (F (+ t (* 1/2 δt)) (+ y (* 1/2 δy1)))))
+    (define δy3 (* δt (F (+ t (* 1/2 δt)) (+ y (* 1/2 δy2)))))
+    (define δy4 (* δt (F (+ t δt) (+ y δy1))))
+    (list (+ t δt)
+          (+ y (* 1/6 (+ δy1 (* 2 δy2) (* 2 δy3) δy4))))))

Task/Runge-Kutta-method/Racket/runge-kutta-method-2.rkt

@@ -0,0 +1,5 @@
+(define ((step-subdivision n method) F h)
+  (λ (x . y) (last (ODE-solve F (cons x y)
+                              #:x-max (+ x h)
+                              #:step (/ h n)
+                              #:method method))))

Task/Runge-Kutta-method/Racket/runge-kutta-method-3.rkt

@@ -0,0 +1,10 @@
+(define (F t y) (* t (sqrt y)))
+
+(define (exact-solution t) (* 1/16 (sqr (+ 4 (sqr t)))))
+
+(define numeric-solution
+    (ODE-solve F '(0 1) #:x-max 10 #:step 1 #:method (step-subdivision 10 RK4)))
+
+(for ([s numeric-solution])
+  (match-define (list t y) s)
+  (printf "t=~a\ty=~a\terror=~a\n" t y (- y (exact-solution t))))

Task/Runge-Kutta-method/Racket/runge-kutta-method-4.rkt

@@ -0,0 +1,4 @@
+> (require plot)
+> (plot (list (function exact-solution 0 10 #:label "Exact solution")
+              (points numeric-solution #:label "Runge-Kutta method"))
+   #:x-label "t" #:y-label "y(t)")