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

Year 2019, Volume: 8 Issue: 2, 451 - 458, 28.06.2019

Derya Arslan

https://doi.org/10.17798/bitlisfen.491847

Cited By: 4

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

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