Comparative Study of Some Numerical and Semi-analytical Methods for Some 1D and 2D Dispersive KdV-type Equations

Abey Sherif KELİL

doi:https://doi.org/10.54974/fcmathsci.1002281

Makale detayları

Comparative Study of Some Numerical and Semi-analytical Methods for Some 1D and 2D Dispersive KdV-type Equations

Yazarlar:

Abey Sherif KELİL

Yayıncı:

Mustafa UÇKUN

Ana Başlıklar:

Matematik

Dergi:

Fundamentals of Contemporary Mathematical Sciences 2022 Vol.3 Issue 1, pp.1-25

Belge Tipi:

Makale

Yayın Tarihi:

1/2022

Belge Dili:

İngilizce

Document ID (Org No.):

2000422257

eISSN:

2717-6185

DOI:

https://doi.org/10.54974/fcmathsci.1002281

Özet:

 

This paper aims to investigate an approximate-analytical and numerical solutions for some 1D
and 2D dispersive homogeneous and non-homogeneous KdV equations by employing two reliable methods namely reduced differential transform method (RDTM) and a classical finite-difference method. RDTM provides an analytical approximate solution in the form of a convergent series. The classical finite-difference method (FDM) to solve dispersive KdV equations is employed by primarily checking Von Neumann’s stability criterion. The performance of the mentioned methods for the considered experiments are compared by computing absolute and relative errors at some spatial nodes at a given time; and to the best of our knowledge, the comparison between these two methods for the considered experiments is novel. Knowledge acquired will enable us to build methods for other related PDEs such as KdV-Burgers, stochastic KdV and fractional KdV-type equations.

Makale detayları

Comparative Study of Some Numerical and Semi-analytical Methods for Some 1D and 2D Dispersive KdV-type Equations

Yazarlar: Abey Sherif KELİL

Yayıncı: Mustafa UÇKUN

Ana Başlıklar: Matematik

Dergi: Fundamentals of Contemporary Mathematical Sciences 2022 Vol.3 Issue 1, pp.1-25

Belge Tipi: Makale

Yayın Tarihi: 1/2022

Belge Dili: İngilizce

Document ID (Org No.): 2000422257

eISSN: 2717-6185

DOI: https://doi.org/10.54974/fcmathsci.1002281

Sayı

Yazarlar:

Abey Sherif KELİL

Yayıncı:

Mustafa UÇKUN

Ana Başlıklar:

Matematik

Dergi:

Fundamentals of Contemporary Mathematical Sciences 2022 Vol.3 Issue 1, pp.1-25

Belge Tipi:

Makale

Yayın Tarihi:

1/2022

Belge Dili:

İngilizce

Document ID (Org No.):

2000422257

eISSN:

2717-6185

DOI:

https://doi.org/10.54974/fcmathsci.1002281