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Update 3_numerical.rst
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source/3_numerical.rst

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@@ -51,7 +51,7 @@ First, compute the intermediate stage vectors:
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.. math::
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\mathbf{k}_i =
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\mathbf{u} \Bigl( \mathbf{x}_n + \Delta t \sum_{j=1}^{i-1} a_{ij}\,\mathbf{k}_j,\,
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\mathbf{u} \Bigl( \mathbf{x}_n + \sigma\,\Delta t \sum_{j=1}^{i-1} a_{ij}\,\mathbf{k}_j,\,
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t_n + c_i \Delta t \Bigr),
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\qquad i = 1, 2, \dots, s,
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@@ -60,7 +60,7 @@ and then update the solution:
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.. math::
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\mathbf{x}_{n+1} =
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\mathbf{x}_n + \Delta t \sum_{i=1}^s b_i\,\mathbf{k}_i.
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\mathbf{x}_n + \sigma\,\Delta t \sum_{i=1}^s b_i\,\mathbf{k}_i.
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Here, the boldface stage variables :math:`\mathbf{k}_i` represent intermediate slope estimates.
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