Zaman Filtresi ile İleri Euler Yönteminin Analizi

Abstract

Bu makale, yeni açık Euler yöntemini basit bir zaman filtresi ile güçlendirmenin etkisini incelemektedir. Değişiklik tamamen modülerdir, yalnızca tek bir ek kod satırı gerektirir ve bu nedenle mevcut hesaplama çerçevelerine kolayca dahil edilebilir. Ortaya çıkan şema, basit bir kararlılık analizi sağlar ve hata için anında bir tahmin sunarken, algoritmadaki her aşamanın rolü kavramsal olarak şeffaf kalır. Zaman filtresinin ileri Euler güncellemesine uygulanması, leaping-frog tipi iki aşamalı, ikinci dereceden doğrusal çok adımlı şemaya cebirsel olarak eşdeğer bir yöntem ortaya çıkarır.

Analysis of Forward Euler Method with Time Filter

Abstract

This papers examines the impact of augmenting the new explicit Euler method with a simple time filter. The modification is fully modular, requiring only a single additional line of code, and can therefore be incorporated easily into existing computational frameworks. The resulting scheme admits straightforward stability analysis and provides an immediate estimation for error, while the role of each stage in the algorithm remains conceptually transparent. Applying the time filter to the forward Euler update yields a method that is algebraically equivalent to a two-step, second-order linear multistep scheme of leap-frog type

Keywords

• Time Filter
• Linear Multistep Method
• Modified Equations

References

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