Some cosmetics & new test added (B5).

src/ODE.jl

@@ -208,14 +208,14 @@ function oderkf{T}(F::Function, tspan::AbstractVector, x0::AbstractVector{T}, p:
             k[j,:] = F(t + h.*c[j], x + h.*(a[j,1:j-1]*k[1:j-1,:]).')
         end
 
-        # compute the 4th order estimate
-        x4 = x + h.*(bs*k).'
+        # compute the (p-1)th order estimate
+        xbs = x + h.*(bs*k).'
 
-        # compute the 5th order estimate
-        x5 = x + h.*(b*k).'
+        # compute the pth order estimate
+        xb = x + h.*(b*k).'
 
         # estimate the local truncation error
-        gamma1 = x5 - x4
+        gamma1 = xb - xbs
 
         # Estimate the error and the acceptable error
         delta = norm(gamma1, Inf)              # actual error
@@ -224,14 +224,14 @@ function oderkf{T}(F::Function, tspan::AbstractVector, x0::AbstractVector{T}, p:
         # Update the solution only if the error is acceptable
         if delta <= tau
             t = t + h
-            x = x5    # <-- using the higher order estimate is called 'local extrapolation'
+            x = xb    # <-- using the higher order estimate is called 'local extrapolation'
             tout = [tout; t]
             xout = [xout; x.']
 
             # Compute the slopes by computing the k[:,j+1]'th column based on the previous k[:,1:j] columns
             # notes: k needs to end up as an Nxs, a is 7x6, which is s by (s-1),
             #        s is the number of intermediate RK stages on [t (t+h)] (Dormand-Prince has s=7 stages)
-            if c[end] == 1 && t != tspan[1]
+            if c[end] == 1 
                 # Assign the last stage for x(k) as the first stage for computing x[k+1].
                 # This is part of the Dormand-Prince pair caveat.
                 # k[:,7] has already been computed, so use it instead of recomputing it

test/perf_test.jl

@@ -1,5 +1,6 @@
 # comparison of adaptive methods
 
+
 # adaptive solvers
 solvers = [
     ODE.ode23,
@@ -10,6 +11,7 @@ solvers = [
     ODE.ode45_ck
     ]
 
+println("\n== problem A3 in DETEST ==\n")
 for solver in solvers
     println("testing method $(string(solver))")
 
@@ -26,4 +28,35 @@ for solver in solvers
     println("*  maximal step: $(maximum(diff(t)))")
 
     println("*  maximal deviation from known solution: $(maximum(abs(y[:]-exp(sin(t)))))\n")
-end
+end
+
+# problem B5 in DETEST
+# motion of a rigid body without external forces
+# (see also Example 1 from http://www.mathworks.se/help/matlab/ref/ode45.html)
+function rigid(t,y)
+	dy = copy(y)
+	dy[1] = y[2] * y[3]
+	dy[2] = -y[1] * y[3]
+	dy[3] = -0.51 * y[1] * y[2]
+
+	return dy
+end
+
+println("\n== problem B5 in DETEST ==\n")
+for solver in solvers
+    println("testing method $(string(solver))")
+
+    # problem B5 in DETEST
+    t,y = solver(rigid, [0.,12.], [0., 1., 1.]);
+    @time begin
+        for i=1:10
+            t,y = solver(rigid, [0.,12.], [0., 1., 1.]);
+        end
+    end
+
+    println("*  number of steps: $(length(t))")
+    println("*  minimal step: $(minimum(diff(t)))")
+    println("*  maximal step: $(maximum(diff(t)))\n")
+
+    # println("*  maximal deviation from known solution: $(maximum(abs(y[:]-exp(sin(t)))))\n")
+end