Look-ahead linear multistep methods for ordinary differential equations : introduction of the method

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Abstract

A new class of discrete variable methods for numerical solution of initial-value problem of ordinary differential equations is proposed. This is an extension of linear multistep methods by a "look-ahead" manner. Basically it consists of a pair of predictor and corrector, including the function value at one more step beyond the present step. Starting with the initial idea of the method, its examples, convergence analysis and stability analysis are described. Future works for establishment of the proposed method are also mentioned.

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