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diff --git a/src/main/java/org/apache/commons/math3/ode/nonstiff/HighamHall54Integrator.java b/src/main/java/org/apache/commons/math3/ode/nonstiff/HighamHall54Integrator.java
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+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package org.apache.commons.math3.ode.nonstiff;
+
+import org.apache.commons.math3.util.FastMath;
+
+
+/**
+ * This class implements the 5(4) Higham and Hall integrator for
+ * Ordinary Differential Equations.
+ *
+ * <p>This integrator is an embedded Runge-Kutta integrator
+ * of order 5(4) used in local extrapolation mode (i.e. the solution
+ * is computed using the high order formula) with stepsize control
+ * (and automatic step initialization) and continuous output. This
+ * method uses 7 functions evaluations per step.</p>
+ *
+ * @since 1.2
+ */
+
+public class HighamHall54Integrator extends EmbeddedRungeKuttaIntegrator {
+
+  /** Integrator method name. */
+  private static final String METHOD_NAME = "Higham-Hall 5(4)";
+
+  /** Time steps Butcher array. */
+  private static final double[] STATIC_C = {
+    2.0/9.0, 1.0/3.0, 1.0/2.0, 3.0/5.0, 1.0, 1.0
+  };
+
+  /** Internal weights Butcher array. */
+  private static final double[][] STATIC_A = {
+    {2.0/9.0},
+    {1.0/12.0, 1.0/4.0},
+    {1.0/8.0, 0.0, 3.0/8.0},
+    {91.0/500.0, -27.0/100.0, 78.0/125.0, 8.0/125.0},
+    {-11.0/20.0, 27.0/20.0, 12.0/5.0, -36.0/5.0, 5.0},
+    {1.0/12.0, 0.0, 27.0/32.0, -4.0/3.0, 125.0/96.0, 5.0/48.0}
+  };
+
+  /** Propagation weights Butcher array. */
+  private static final double[] STATIC_B = {
+    1.0/12.0, 0.0, 27.0/32.0, -4.0/3.0, 125.0/96.0, 5.0/48.0, 0.0
+  };
+
+  /** Error weights Butcher array. */
+  private static final double[] STATIC_E = {
+    -1.0/20.0, 0.0, 81.0/160.0, -6.0/5.0, 25.0/32.0, 1.0/16.0, -1.0/10.0
+  };
+
+  /** Simple constructor.
+   * Build a fifth order Higham and Hall integrator with the given step bounds
+   * @param minStep minimal step (sign is irrelevant, regardless of
+   * integration direction, forward or backward), the last step can
+   * be smaller than this
+   * @param maxStep maximal step (sign is irrelevant, regardless of
+   * integration direction, forward or backward), the last step can
+   * be smaller than this
+   * @param scalAbsoluteTolerance allowed absolute error
+   * @param scalRelativeTolerance allowed relative error
+   */
+  public HighamHall54Integrator(final double minStep, final double maxStep,
+                                final double scalAbsoluteTolerance,
+                                final double scalRelativeTolerance) {
+    super(METHOD_NAME, false, STATIC_C, STATIC_A, STATIC_B, new HighamHall54StepInterpolator(),
+          minStep, maxStep, scalAbsoluteTolerance, scalRelativeTolerance);
+  }
+
+  /** Simple constructor.
+   * Build a fifth order Higham and Hall integrator with the given step bounds
+   * @param minStep minimal step (sign is irrelevant, regardless of
+   * integration direction, forward or backward), the last step can
+   * be smaller than this
+   * @param maxStep maximal step (sign is irrelevant, regardless of
+   * integration direction, forward or backward), the last step can
+   * be smaller than this
+   * @param vecAbsoluteTolerance allowed absolute error
+   * @param vecRelativeTolerance allowed relative error
+   */
+  public HighamHall54Integrator(final double minStep, final double maxStep,
+                                final double[] vecAbsoluteTolerance,
+                                final double[] vecRelativeTolerance) {
+    super(METHOD_NAME, false, STATIC_C, STATIC_A, STATIC_B, new HighamHall54StepInterpolator(),
+          minStep, maxStep, vecAbsoluteTolerance, vecRelativeTolerance);
+  }
+
+  /** {@inheritDoc} */
+  @Override
+  public int getOrder() {
+    return 5;
+  }
+
+  /** {@inheritDoc} */
+  @Override
+  protected double estimateError(final double[][] yDotK,
+                                 final double[] y0, final double[] y1,
+                                 final double h) {
+
+    double error = 0;
+
+    for (int j = 0; j < mainSetDimension; ++j) {
+      double errSum = STATIC_E[0] * yDotK[0][j];
+      for (int l = 1; l < STATIC_E.length; ++l) {
+        errSum += STATIC_E[l] * yDotK[l][j];
+      }
+
+      final double yScale = FastMath.max(FastMath.abs(y0[j]), FastMath.abs(y1[j]));
+      final double tol = (vecAbsoluteTolerance == null) ?
+                         (scalAbsoluteTolerance + scalRelativeTolerance * yScale) :
+                         (vecAbsoluteTolerance[j] + vecRelativeTolerance[j] * yScale);
+      final double ratio  = h * errSum / tol;
+      error += ratio * ratio;
+
+    }
+
+    return FastMath.sqrt(error / mainSetDimension);
+
+  }
+
+}