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diff --git a/src/main/java/org/apache/commons/math3/ode/nonstiff/AdamsFieldIntegrator.java b/src/main/java/org/apache/commons/math3/ode/nonstiff/AdamsFieldIntegrator.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.Field;
+import org.apache.commons.math3.RealFieldElement;
+import org.apache.commons.math3.exception.DimensionMismatchException;
+import org.apache.commons.math3.exception.MaxCountExceededException;
+import org.apache.commons.math3.exception.NoBracketingException;
+import org.apache.commons.math3.exception.NumberIsTooSmallException;
+import org.apache.commons.math3.linear.Array2DRowFieldMatrix;
+import org.apache.commons.math3.ode.FieldExpandableODE;
+import org.apache.commons.math3.ode.FieldODEState;
+import org.apache.commons.math3.ode.FieldODEStateAndDerivative;
+import org.apache.commons.math3.ode.MultistepFieldIntegrator;
+
+
+/** Base class for {@link AdamsBashforthFieldIntegrator Adams-Bashforth} and
+ * {@link AdamsMoultonFieldIntegrator Adams-Moulton} integrators.
+ * @param <T> the type of the field elements
+ * @since 3.6
+ */
+public abstract class AdamsFieldIntegrator<T extends RealFieldElement<T>> extends MultistepFieldIntegrator<T> {
+
+    /** Transformer. */
+    private final AdamsNordsieckFieldTransformer<T> transformer;
+
+    /**
+     * Build an Adams integrator with the given order and step control parameters.
+     * @param field field to which the time and state vector elements belong
+     * @param name name of the method
+     * @param nSteps number of steps of the method excluding the one being computed
+     * @param order order of the method
+     * @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
+     * @exception NumberIsTooSmallException if order is 1 or less
+     */
+    public AdamsFieldIntegrator(final Field<T> field, final String name,
+                                final int nSteps, final int order,
+                                final double minStep, final double maxStep,
+                                final double scalAbsoluteTolerance,
+                                final double scalRelativeTolerance)
+        throws NumberIsTooSmallException {
+        super(field, name, nSteps, order, minStep, maxStep,
+              scalAbsoluteTolerance, scalRelativeTolerance);
+        transformer = AdamsNordsieckFieldTransformer.getInstance(field, nSteps);
+    }
+
+    /**
+     * Build an Adams integrator with the given order and step control parameters.
+     * @param field field to which the time and state vector elements belong
+     * @param name name of the method
+     * @param nSteps number of steps of the method excluding the one being computed
+     * @param order order of the method
+     * @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
+     * @exception IllegalArgumentException if order is 1 or less
+     */
+    public AdamsFieldIntegrator(final Field<T> field, final String name,
+                                final int nSteps, final int order,
+                                final double minStep, final double maxStep,
+                                final double[] vecAbsoluteTolerance,
+                                final double[] vecRelativeTolerance)
+        throws IllegalArgumentException {
+        super(field, name, nSteps, order, minStep, maxStep,
+              vecAbsoluteTolerance, vecRelativeTolerance);
+        transformer = AdamsNordsieckFieldTransformer.getInstance(field, nSteps);
+    }
+
+    /** {@inheritDoc} */
+    public abstract FieldODEStateAndDerivative<T> integrate(final FieldExpandableODE<T> equations,
+                                                            final FieldODEState<T> initialState,
+                                                            final T finalTime)
+        throws NumberIsTooSmallException, DimensionMismatchException,
+               MaxCountExceededException, NoBracketingException;
+
+    /** {@inheritDoc} */
+    @Override
+    protected Array2DRowFieldMatrix<T> initializeHighOrderDerivatives(final T h, final T[] t,
+                                                                      final T[][] y,
+                                                                      final T[][] yDot) {
+        return transformer.initializeHighOrderDerivatives(h, t, y, yDot);
+    }
+
+    /** Update the high order scaled derivatives for Adams integrators (phase 1).
+     * <p>The complete update of high order derivatives has a form similar to:
+     * <pre>
+     * r<sub>n+1</sub> = (s<sub>1</sub>(n) - s<sub>1</sub>(n+1)) P<sup>-1</sup> u + P<sup>-1</sup> A P r<sub>n</sub>
+     * </pre>
+     * this method computes the P<sup>-1</sup> A P r<sub>n</sub> part.</p>
+     * @param highOrder high order scaled derivatives
+     * (h<sup>2</sup>/2 y'', ... h<sup>k</sup>/k! y(k))
+     * @return updated high order derivatives
+     * @see #updateHighOrderDerivativesPhase2(RealFieldElement[], RealFieldElement[], Array2DRowFieldMatrix)
+     */
+    public Array2DRowFieldMatrix<T> updateHighOrderDerivativesPhase1(final Array2DRowFieldMatrix<T> highOrder) {
+        return transformer.updateHighOrderDerivativesPhase1(highOrder);
+    }
+
+    /** Update the high order scaled derivatives Adams integrators (phase 2).
+     * <p>The complete update of high order derivatives has a form similar to:
+     * <pre>
+     * r<sub>n+1</sub> = (s<sub>1</sub>(n) - s<sub>1</sub>(n+1)) P<sup>-1</sup> u + P<sup>-1</sup> A P r<sub>n</sub>
+     * </pre>
+     * this method computes the (s<sub>1</sub>(n) - s<sub>1</sub>(n+1)) P<sup>-1</sup> u part.</p>
+     * <p>Phase 1 of the update must already have been performed.</p>
+     * @param start first order scaled derivatives at step start
+     * @param end first order scaled derivatives at step end
+     * @param highOrder high order scaled derivatives, will be modified
+     * (h<sup>2</sup>/2 y'', ... h<sup>k</sup>/k! y(k))
+     * @see #updateHighOrderDerivativesPhase1(Array2DRowFieldMatrix)
+     */
+    public void updateHighOrderDerivativesPhase2(final T[] start, final T[] end,
+                                                 final Array2DRowFieldMatrix<T> highOrder) {
+        transformer.updateHighOrderDerivativesPhase2(start, end, highOrder);
+    }
+
+}