Improved rk4 integration to allow longer time interval than 1 step.

matrix/integration.hpp

@@ -10,18 +10,33 @@ int integrate_rk4(
     const Matrix<Type, M, 1> & y0,
     const Matrix<Type, N, 1> & u,
     Type t0,
-    Type h,
+    Type tf,
+    Type h0,
     Matrix<Type, M, 1> & y1
 )
 {
     // https://en.wikipedia.org/wiki/Runge%E2%80%93Kutta_methods
+    Type t1 = t0;
+    y1 = y0;
+    Type h = h0;
     Vector<Type, M> k1, k2, k3, k4;
-    k1 = f(t0, y0, u);
-    k2 = f(t0 + h/2, y0 + k1*h/2, u);
-    k3 = f(t0 + h/2, y0 + k2*h/2, u);
-    k4 = f(t0 + h, y0 + k3*h, u);
-    y1 = y0 + (k1 + k2*2 + k3*2 + k4)*(h/6);
+    if (tf < t0) return -1; // make sure t1 > t0
+    while (t1 < tf) {
+        if (t1 + h0 < tf) {
+            h = h0;
+        } else {
+            h = tf - t1;
+        }
+        k1 = f(t1, y1, u);
+        k2 = f(t1 + h/2, y1 + k1*h/2, u);
+        k3 = f(t1 + h/2, y1 + k2*h/2, u);
+        k4 = f(t1 + h, y1 + k3*h, u);
+        y1 += (k1 + k2*2 + k3*2 + k4)*(h/6);
+        t1 += h;
+    }
     return 0;
 }
 
 } // namespace matrix
+
+// vim: set et fenc=utf-8 ff=unix sts=0 sw=4 ts=4 :