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diff --git a/src/main/java/org/apache/commons/math3/ode/nonstiff/EulerFieldStepInterpolator.java b/src/main/java/org/apache/commons/math3/ode/nonstiff/EulerFieldStepInterpolator.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.ode.FieldEquationsMapper;
+import org.apache.commons.math3.ode.FieldODEStateAndDerivative;
+
+/**
+ * This class implements a linear interpolator for step.
+ *
+ * <p>This interpolator computes dense output inside the last
+ * step computed. The interpolation equation is consistent with the
+ * integration scheme :
+ * <ul>
+ *   <li>Using reference point at step start:<br>
+ *     y(t<sub>n</sub> + &theta; h) = y (t<sub>n</sub>) + &theta; h y'
+ *   </li>
+ *   <li>Using reference point at step end:<br>
+ *     y(t<sub>n</sub> + &theta; h) = y (t<sub>n</sub> + h) - (1-&theta;) h y'
+ *   </li>
+ * </ul>
+ * </p>
+ *
+ * where &theta; belongs to [0 ; 1] and where y' is the evaluation of
+ * the derivatives already computed during the step.</p>
+ *
+ * @see EulerFieldIntegrator
+ * @param <T> the type of the field elements
+ * @since 3.6
+ */
+
+class EulerFieldStepInterpolator<T extends RealFieldElement<T>>
+    extends RungeKuttaFieldStepInterpolator<T> {
+
+    /** Simple constructor.
+     * @param field field to which the time and state vector elements belong
+     * @param forward integration direction indicator
+     * @param yDotK slopes at the intermediate points
+     * @param globalPreviousState start of the global step
+     * @param globalCurrentState end of the global step
+     * @param softPreviousState start of the restricted step
+     * @param softCurrentState end of the restricted step
+     * @param mapper equations mapper for the all equations
+     */
+    EulerFieldStepInterpolator(final Field<T> field, final boolean forward,
+                                             final T[][] yDotK,
+                                             final FieldODEStateAndDerivative<T> globalPreviousState,
+                                             final FieldODEStateAndDerivative<T> globalCurrentState,
+                                             final FieldODEStateAndDerivative<T> softPreviousState,
+                                             final FieldODEStateAndDerivative<T> softCurrentState,
+                                             final FieldEquationsMapper<T> mapper) {
+        super(field, forward, yDotK,
+              globalPreviousState, globalCurrentState, softPreviousState, softCurrentState,
+              mapper);
+    }
+
+    /** {@inheritDoc} */
+    @Override
+    protected EulerFieldStepInterpolator<T> create(final Field<T> newField, final boolean newForward, final T[][] newYDotK,
+                                                                 final FieldODEStateAndDerivative<T> newGlobalPreviousState,
+                                                                 final FieldODEStateAndDerivative<T> newGlobalCurrentState,
+                                                                 final FieldODEStateAndDerivative<T> newSoftPreviousState,
+                                                                 final FieldODEStateAndDerivative<T> newSoftCurrentState,
+                                                                 final FieldEquationsMapper<T> newMapper) {
+        return new EulerFieldStepInterpolator<T>(newField, newForward, newYDotK,
+                                                 newGlobalPreviousState, newGlobalCurrentState,
+                                                 newSoftPreviousState, newSoftCurrentState,
+                                                 newMapper);
+    }
+
+    /** {@inheritDoc} */
+    @SuppressWarnings("unchecked")
+    @Override
+    protected FieldODEStateAndDerivative<T> computeInterpolatedStateAndDerivatives(final FieldEquationsMapper<T> mapper,
+                                                                                   final T time, final T theta,
+                                                                                   final T thetaH, final T oneMinusThetaH) {
+        final T[] interpolatedState;
+        final T[] interpolatedDerivatives;
+        if (getGlobalPreviousState() != null && theta.getReal() <= 0.5) {
+            interpolatedState       = previousStateLinearCombination(thetaH);
+            interpolatedDerivatives = derivativeLinearCombination(time.getField().getOne());
+        } else {
+            interpolatedState       = currentStateLinearCombination(oneMinusThetaH.negate());
+            interpolatedDerivatives = derivativeLinearCombination(time.getField().getOne());
+        }
+
+        return new FieldODEStateAndDerivative<T>(time, interpolatedState, interpolatedDerivatives);
+
+    }
+
+}