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diff --git a/src/main/java/org/apache/commons/math3/ode/nonstiff/GillFieldIntegrator.java b/src/main/java/org/apache/commons/math3/ode/nonstiff/GillFieldIntegrator.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;
+import org.apache.commons.math3.util.MathArrays;
+
+
+/**
+ * This class implements the Gill fourth order Runge-Kutta
+ * integrator for Ordinary Differential Equations .
+
+ * <p>This method is an explicit Runge-Kutta method, its Butcher-array
+ * is the following one :
+ * <pre>
+ *    0  |    0        0       0      0
+ *   1/2 |   1/2       0       0      0
+ *   1/2 | (q-1)/2  (2-q)/2    0      0
+ *    1  |    0       -q/2  (2+q)/2   0
+ *       |-------------------------------
+ *       |   1/6    (2-q)/6 (2+q)/6  1/6
+ * </pre>
+ * where q = sqrt(2)</p>
+ *
+ * @see EulerFieldIntegrator
+ * @see ClassicalRungeKuttaFieldIntegrator
+ * @see MidpointFieldIntegrator
+ * @see ThreeEighthesFieldIntegrator
+ * @see LutherFieldIntegrator
+ * @param <T> the type of the field elements
+ * @since 3.6
+ */
+
+public class GillFieldIntegrator<T extends RealFieldElement<T>>
+    extends RungeKuttaFieldIntegrator<T> {
+
+    /** Simple constructor.
+     * Build a fourth-order Gill integrator with the given step.
+     * @param field field to which the time and state vector elements belong
+     * @param step integration step
+     */
+    public GillFieldIntegrator(final Field<T> field, final T step) {
+        super(field, "Gill", step);
+    }
+
+    /** {@inheritDoc} */
+    public T[] getC() {
+        final T[] c = MathArrays.buildArray(getField(), 3);
+        c[0] = fraction(1, 2);
+        c[1] = c[0];
+        c[2] = getField().getOne();
+        return c;
+    }
+
+    /** {@inheritDoc} */
+    public T[][] getA() {
+
+        final T two     = getField().getZero().add(2);
+        final T sqrtTwo = two.sqrt();
+
+        final T[][] a = MathArrays.buildArray(getField(), 3, -1);
+        for (int i = 0; i < a.length; ++i) {
+            a[i] = MathArrays.buildArray(getField(), i + 1);
+        }
+        a[0][0] = fraction(1, 2);
+        a[1][0] = sqrtTwo.subtract(1).multiply(0.5);
+        a[1][1] = sqrtTwo.subtract(2).multiply(-0.5);
+        a[2][0] = getField().getZero();
+        a[2][1] = sqrtTwo.multiply(-0.5);
+        a[2][2] = sqrtTwo.add(2).multiply(0.5);
+        return a;
+    }
+
+    /** {@inheritDoc} */
+    public T[] getB() {
+
+        final T two     = getField().getZero().add(2);
+        final T sqrtTwo = two.sqrt();
+
+        final T[] b = MathArrays.buildArray(getField(), 4);
+        b[0] = fraction(1, 6);
+        b[1] = sqrtTwo.subtract(2).divide(-6);
+        b[2] = sqrtTwo.add(2).divide(6);
+        b[3] = b[0];
+
+        return b;
+
+    }
+
+    /** {@inheritDoc} */
+    @Override
+    protected GillFieldStepInterpolator<T>
+        createInterpolator(final boolean forward, T[][] yDotK,
+                           final FieldODEStateAndDerivative<T> globalPreviousState,
+                           final FieldODEStateAndDerivative<T> globalCurrentState,
+                           final FieldEquationsMapper<T> mapper) {
+        return new GillFieldStepInterpolator<T>(getField(), forward, yDotK,
+                                                globalPreviousState, globalCurrentState,
+                                                globalPreviousState, globalCurrentState,
+                                                mapper);
+    }
+
+}