Two-step family of "Look-ahead" linear multistep method for ODEs

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Abstract

A family of two-step "look-ahead" linear multistep methods (LALMM) is formulated and analysed. LALMM is a new class of discrete variable methods for numerical solution of initial-value problem of ordinary differential equations (ODEs). Two fourth-order pairs of predictor and corrector are derived and showed to be A(Θ)-stable. The obtained schemes provide the basis for futher developement of LALMM.

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