explained test rationale

git-svn-id: https://svn.apache.org/repos/asf/commons/proper/math/trunk@919172 13f79535-47bb-0310-9956-ffa450edef68

src/test/java/org/apache/commons/math/ode/jacobians/FirstOrderIntegratorWithJacobiansTest.java

@@ -31,6 +31,15 @@ public class FirstOrderIntegratorWithJacobiansTest {
     @Test
     public void testLowAccuracyExternalDifferentiation()
         throws IntegratorException, DerivativeException {
+        // this test does not really test FirstOrderIntegratorWithJacobians,
+        // it only shows the WITHOUT this class, attempting to recover
+        // the jacobians from external differentiation on simple integration
+        // results with loo accuracy gives very poor results. In fact,
+        // the curves dy/dp = g(b) when b varies from 2.88 to 3.08 are
+        // essentially noise.
+        // This test is taken from Heirer, Norsett and Wanner book
+        // Solving Ordinary Differential Equations I (Nonstiff problems),
+        // the curves dy/dp = g(b) are in figure 6.5
         FirstOrderIntegrator integ =
             new DormandPrince54Integrator(1.0e-8, 100.0, 1.0e-4, 1.0e-4);
         double hP = 1.0e-12;