Numerical Verification of ordinary differential equations using Affine Arithmetic and Mean Value Form(Theory)

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  • 平均値形式とアフィン演算を用いた常微分方程式の精度保証法(理論)
  • 平均値形式とアフィン演算を用いた常微分方程式の精度保証法
  • ヘイキンチ ケイシキ ト アフィン エンザン オ モチイタ ジョウ ビブン ホウテイシキ ノ セイド ホショウホウ

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Abstract

When we solve IVPs of ODEs with guaranteed accuracy, we have some problems about explosion of interval width and calculating cost, especially in the case of ODEs which is sensitive with initial value such as Lorenz equation. In this paper, we propose an accurate and fast method for IVPs using power series arithmetic, mean value form and affne arithmetic. Moreover, we show the efficiency of our method through some numerical examples and comparison with Lohner's AWA package.

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