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Journals / Afyon Kocatepe Üniversitesi Fen ve Mühendislik Bilimleri Dergisi / 2019 / Cilt: 19 Sayı: 3

Stabilized Finite Element Methods for Predator-Prey Systems

Av-Avcı Problemleri için Kararlı Sonlu Eleman Yöntemleri Üzerine Bir Not

Ali Şendur(ALANYA ALAADDIN KEYKUBAT UNIVERSITY)0000-0001-8628-5497
Pages
653–661
Publication Date
2019-12-31
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

The numerical results depict that the algorithm is efficient and feasible

📌 3 Key Takeaways

🎯
Objective & Hypothesis:A numerical method that will improve and produce effective results for solving mathematical model for the system of predator-prey interactions which is defined by convection-diffusion-reaction problem is studied herein.
📊
Key Findings & Data:We consider the Pseudo Residual-free Bubble (PRFB) method which is based on augmenting the finite element space by a set appropriate functions for the space discretization.
💡
Conclusion & Impact:The numerical results depict that the algorithm is efficient and feasible
🔬Design:Modeling & Simulation
📍Scope:Comprehensive Sample
⚙️Variables:Av-avcı denklem sistemleri · Konveksiyon-difüzyon-reaksiyon · Kararlı Sonlu Eleman Yöntemi

Abstract

A numerical method that will improve and produce effective results for solving mathematical model for the system of predator-prey interactions which is defined by convection-diffusion-reaction problem is studied herein. We consider the Pseudo Residual-free Bubble (PRFB) method which is based on augmenting the finite element space by a set appropriate functions for the space discretization. The method is applied on different test problems and the numerical solutions are in good agreement with the result available in literature. The numerical results depict that the algorithm is efficient and feasible

Özet

Bu çalışmada, konveksiyon-difüzyon-reaksiyon problemleri ile modellenebilen av-avcı denklem sistemlerinin simülasyonunda kullanılan sayısal çözüm tekniklerini iyileştirecek ve daha etkin sonuçlar üretecek sayısal bir yöntem önerilmiştir. Uzay ayrıklaştırması için, sonlu elemanlar metodunu uygularken seçilen polinom baz fonksiyonlarına ilaveten fonksiyon uzayının özel tip fonksiyonlarla (residual-free bubbles) zenginleştirilmesine dayanan Pseudo Residual-free Bubble (PRFB) yöntemi kullanılmıştır. Söz konusu yöntem, çeşitli test örneklerine uygulanmış olup elde edilen sayısal çözümlerin, literatürde mevcut olan sonuçlar ile iyi bir uyum içinde olduğu gözlemlenmiştir. Sayısal sonuçlar, önerilen yöntemin verimli ve uygulanabilir olduğunu göstermektedir.

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Cite This Article

Şendur, A. (2019). Stabilized Finite Element Methods for Predator-Prey Systems. Afyon Kocatepe Üniversitesi Fen ve Mühendislik Bilimleri Dergisi, Cilt: 19 Sayı: 3, 653–661. https://doi.org/10.35414/akufemubid.597506

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