Abstract
A family of numerical methods is developed for the solution of the general initial value problem y ( N) ( t) = f( t, y, y t , …, y ( N−1) ), t> t 0, with y( t 0, y ( r) ( t 0) given ( r = 1, 2, …, N−1). The orders of the methods are seen to be one or two and global extrapolation is used to increase the order of a given method by one or two powers. The methods are tested on the Blasius nonlinear third-order initial value problem and on a linear fourth-order problem from ship dynamics.
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