Kesirli Mertebeden Pseudo Hiperbolik Diferansiyel Denklemlerin Sonlu Fark Metodu ile Nümerik Çözümleri

Year 2022, Volume: 22 Issue: 5, 998 - 1004, 27.10.2022

Fatih Özbağ Mahmut Modanlı

https://doi.org/10.35414/akufemubid.1124445

Abstract

Kesirli mertebeden diferansiyel denklemler mühendislik, fizik ve biyoloji gibi alanlarda matematiksel problemlerin modellenmesinde önemli yer almaktadır. Bu makalede kesirli mertebeden pseudo hiperbolik diferansiyel denklemler için bir başlangıç sınır değer probleminin sonlu fark metodu ile yaklaşık çözümleri araştırılmıştır. İlk olarak başlangıç sınır değer problemi için birinci mertebeden sonlu fark şeması oluşturulmuştur. Daha sonra bu sonlu fark şeması için kararlılık analizi yapılmıştır. Elde edilen teorik sonuçları desteklemek için örnek bir problemin farklı kesirli mertebeden türevlerinde gerçek ve yaklaşık çözümler için hata değerleri hesaplanmıştır. Uygulanan çözüm metodunun etkinliğini göstermek için bazı nümerik simülasyonlar verilmiştir.

Keywords

Kesirli Mertebeden Pseudo Hiperbolik Denklem, Sonlu Fark Metodu, Nümerik Çözüm, Kararlık

Numerical Solutions of Fractional Order Pseudo Hyperbolic Differential Equations by Finite Difference Method

Abstract

Fractional differential equations are useful for modelling mathematical issues in fields including engineering, physics, and biology. In this article, approximate solutions of an initial boundary value problem for fractional pseudo hyperbolic differential equations are investigated using the finite difference method. First, a first-order finite difference scheme is created for the initial boundary value problem. Then, stability analysis was performed for this finite difference scheme. In order to support the theoretical results obtained, error values were calculated for precise and approximate solutions in different fractional order derivatives of a sample problem. Some numerical simulations are also given to show the effectiveness of the applied solution method.

Keywords

Fractional Order Pseudo Hyperbolic Equation, Finite Difference Method, Numerical Solutions, Stability

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