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

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.

A Note on Stabilized Finite Element Methods for Predator-Prey Systems

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

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