Semi-Analytical Solutions of Nonlinear Equation Modelling Reaction in a Dispersive Medium
Özet
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 understandthe sensitivity of homotopy based methods in solving the proposed reaction-dispersion equation. Using symbolic computation withcarefully chosen perturbation parameters, the semi-analytical solutions are compared with the exact solutions, in order to show theefficiency of homotopy and Padé techniques. Obtained solutions, which can play key role in modelling reaction in a dispersive medium,are illustrated and discussed. 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.
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https://app.trdizin.gov.tr/makale/TXpJd05USTRPQT09https://hdl.handle.net/20.500.11776/7334
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