论文信息 - A family of numerical methods for the solution of high-order general initial value problem

A family of numerical methods for the solution of high-order general initial value problem

Abstract A family of numerical methods is developed for the solution of the general initial value problem y(N)(t) = f(t, y, yt, …, y(N−1)), t>t0, with y(t0, y(r)(t0) 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.

E. H. Twizell

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