A Fully Implicit Finite Difference Approach for Numerical Solution of the Generalized Equal Width (GEW) Equation

İNAN, BİLGE; BAHADIR, AHMET

doi:10.1007/s40010-019-00594-8

A Fully Implicit Finite Difference Approach for Numerical Solution of the Generalized Equal Width (GEW) Equation

PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES INDIA SECTION A-PHYSICAL SCIENCES, cilt.90, sa.2, ss.299-308, 2020 (SCI-Expanded)

Yayın Türü: Makale / Tam Makale
Cilt numarası: 90 Sayı: 2
Basım Tarihi: 2020
Doi Numarası: 10.1007/s40010-019-00594-8
Dergi Adı: PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES INDIA SECTION A-PHYSICAL SCIENCES
Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, INSPEC, zbMATH
Sayfa Sayıları: ss.299-308
İnönü Üniversitesi Adresli: Evet

Özet

In this paper, a fully implicit finite difference method is presented to solve the generalized equal width equation. This implicit method allows to handle any values of p. Since the equation is nonlinear the scheme leads to a system of nonlinear equations. At each time step, Newton's method is used to solve this nonlinear system. The linear stability analysis of the proposed method is investigated using von Neumann approach and at the end of this investigation is seen that the method is unconditionally stable. The results are comparisons with analytical and other numerical values clearly show that results obtained using the fully implicit finite difference scheme are precise and reliable.