Javad FARZİ, Mevlüde YAKIT ONGUN, Damla ARSLAN

Kesirli Mertebeden Otokatalitik Reaksiyon Modelinin Nümerik Çözümleri

Bu makale kesirli mertebeden otokatalitik kimyasal modelin nümerik çözümleri ile ilgilidir. Model 0 ൏ ߙ ൏ 1 için ߙ kesirli mertebeden lineer olmayan bir diferansiyel denklem sistemidir. Çokadımlı yöntemlere dayanan (açık ve kapalı), standart olmayan sonlu fark yöntemi ve integral çarpanı yöntemi (PI) olmak üzere üç farklı nümerik yöntem geliştirilmiştir. İlk iki yöntem diferansiyel denklem modeline ve PI yöntemi model problemin integral denklem formulasyonuna dayanmaktadır. Geliştirilen yöntemlerin tamlığı, etkinliği ve bazı sayısal karşılaştırılmaları nümerik sonuçlarla gösterilmiştir.

Numerical Solutions of Fractional Order Autocatalytic Chemical Reaction Model

The main concern of this paper is the study and the development of numerical methods for solving fractional order autocatalytic chemical reaction model problem. This is a nonlinear fractional order differential equation of fractional order ߙ ,where 0 ൏ ߙ ൏ 1. Three different (explicit and implicit) schemes based on multistep methods, nonstandard finite difference method and the product integration (PI) method are developed. The first two schemes are based on differential equation model and the PI scheme is constructed by the integral equation formulation of the model problem. The accuracy, efficiency and some numerical comparisons of the developed methods are demonstrated in numerical results.

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