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

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概要

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• 常微分方程式の初期値問題に対する数値解法として,離散変数法の新しいクラスを提案する.これは線型多段階法を「先読み」型に拡張するものである.その基本的な考え方は,現在のステップ点を一つ超えたステップ点での函数値計算を含む予測子と修正子の組を構成するものである.この方法の考え方の出発点から説き起こし,その実例,収束性の解析,安定性解析を述べる.提案する方法を確立するための課題についても言及する.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.

著者

• Mitsui Taketomo

  Department of Mathematical Sciences, Faculty of Science & Engineering, Doshisha University

• Mitsui Taketomo

  Department Of Mathematical Science Faculty Of Science & Engineering Doshisha University

• Mitsui Taketomo

  Department Of Mathematical Sciences Faculty Of Science & Engineering Doshisha University

関連論文

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