In view of tedious calculations involved in deriving Runge–kutta methods of higher order, we shall derive only methods of order upto three and quote same well known methods of order four. We may recall that the Taylor's method of order p can be written in the form (3.11) with
 |
(3.16) |
where
The equation (3.16) can also be written as
 |
(3.17) |
where
 |
(3.18) |
We also write
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