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


İNAN B., BAHADIR A. R.

PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES INDIA SECTION A-PHYSICAL SCIENCES, cilt.90, ss.299-308, 2020 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 90 Konu: 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
  • Sayfa Sayıları: ss.299-308

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.