Approximate Solutions of Singularly Perturbed Nonlinear Ill-posed and Sixth-order Boussinesq Equations with Hybrid Method

Abstract

The aim of this paper is to obtain the approximate solution of singularly perturbed ill-posed and sixth-order Boussinesq equation by hybrid method (differential transform and finite difference method) as a different alternative method. Differential transform method is applied for 𝑡 −time variable and the finite difference method (central difference approach) is applied for 𝑥 −position variable. Two examples are presented to demonstrate the efficiency and reliability of the hybrid method. Numerical results are given and compared with exact solution and in literature RDTM solution. The numerical data show that hybrid method is a powerful, quite efficient and is practically well suited for solving nonlinear singular perturbed Boussinesq equations.

Keywords

• Sixth-order Boussinesq Equation,Differential Transform Method,Finite Difference Method,Approximate Solution

Hibrit Metot ile Singüler Pertürbe Nonlineer Ill-posed ve Altıncı Mertebe Boussinesq Denklemlerinin Yaklaşık Çözümleri

Abstract

Bu çalışmanın amacı, singüler pertürbe lineer olmayan ill-posed ve altıncı mertebeden Boussinesq denkleminin farklı bir alternatif yöntem olan hibrit metotla (diferansiyel dönüşüm ve sonlu fark metodu) yaklaşık çözümünü elde etmektir. 𝑡 −zaman değişkeni için diferansiyel dönüşüm metodu ve 𝑥 −konum değişkeni için sonlu fark metodu (merkezi fark yaklaşımı) uygulanmıştır. Hibrit yöntemin etkinliğini ve güvenilirliğini göstermek için iki örnek sunulmuştur. Nümerik sonuçlar, kesin çözüm ve literatürde yer alan RDTM çözümü ile karşılaştırılmıştır. Sayısal veriler bu yöntemin güçlü, oldukça etkili olduğunu ve nonlineer singüler pertürbe Boussinesq denklemlerini çözmek için pratik olarak uygun olduğunu göstermektedir.

Keywords

• Altıncı Mertebe Boussinesq Denklemi,Ill-posed Boussinesq Denklemi,Diferansiyel Dönüşüm Metodu,Sonlu Fark Metodu,Yaklaşık Çözüm

References

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