Dağılımlı Bir Ortamda Doğrusal Olmayan Reaksiyon Model Denkleminin Yarı Analitik Çözümleri

Yıl 2018, Cilt: 8 Sayı: 1, 197 - 202, 01.01.2018

Zehra Pinar Hüseyin Kocak Yasser Daoud

Öz

Bu çalışma, üçüncü mertebeden reaksiyon terimli dağılım dispersive denkleminin yarı analitik çözümlerini üzerinedir. Son zamanlarda ele alınan problem literatürde tam olarak çözülmüştür. Ayrıca, yarı analitik çözümler, önerilen reaksiyon-dağılım denkleminin çözümünde homotopi temelli yöntemlerin hassasiyetini anlamak için gereklidir. Seçilen pertürbasyon parametreleri ile sembolik hesaplama kullanarak, yarı analitik çözümler, homotopi ve Padé tekniklerinin verimliliğini göstermek için kesin çözümlerle karşılaştırılmaktadır. Elde edilen çözümler dağılımlı ortamda reaksiyon modellemesinde büyük rol oynamaktadır

Anahtar Kelimeler

Homotopi analiz metodu, Padé yaklaşımı, Reaksiyon-dağılım denklemi, Yarı-analitik çözümler

Semi-analytical solutions of nonlinear equation modelling reaction in a dispersive medium

Öz

This study explores the semi-analytical solutions of the third-order dispersive equation with reaction Fisher-like term. Recently, the proposed problem has been exactly solved in the literature. Additionally, the semi-analytical solutions are needed to understand the sensitivity of homotopy based methods in solving the proposed reaction-dispersion equation. Using symbolic computation with carefully chosen perturbation parameters, the semi-analytical solutions are compared with the exact solutions, in order to show the efficiency of homotopy and Padé techniques. Obtained solutions, which can play key role in modelling reaction in a dispersive medium, are illustrated and discussed.

Anahtar Kelimeler

Reaction-dispersion equation, Homotopy Analysis Method, Padé approximation, Semi-analytical solutions

Kaynakça

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