A local radial basis function-finite difference (RBF-FD) method for solving 1D and 2D coupled Schrödinger-Boussinesq (SBq) equations

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Tarih

2021

Dergi Başlığı

Dergi ISSN

Cilt Başlığı

Yayıncı

Elsevier

Erişim Hakkı

info:eu-repo/semantics/closedAccess

Özet

In this study, one-dimensional (1D) and two-dimensional (2D) coupled Schrodinger-Boussinesq (SBq) equations are examined numerically. A local meshless method based on radial basis function-finite difference (RBF-FD) method for spatial approximation is devised. We use polyharmonic splines as radial basis function along with augmented polynomials. By using polyharmonic splines we avoid to choose optimal shape parameter which requires special algorithms in meshless methods. For temporal discretization, low-storage ten-stage fourth-order explicit strong stability preserving Runge Kutta method is used which gives more flexibility on temporal step width. L-infinity and L-2 error norms are calculated to show accuracy of the proposed method. Further, conserved quantities are monitoried during numerical simulations to see how good the proposed method preserves them. Stability of the proposed method is dicussed numerically. Some codes are developed in Julia programming language to achieve more speed up in numerical simulations. Obtained results and their comparison with some studies such as wavelet, difference schemes and Fourier spectral methods available in literature verify the efficiency and reliability of the proposed method.

Açıklama

WOS:000656660200004

Anahtar Kelimeler

Coupled Schrödinger-Boussinesq (SBq) equations, Local meshless method, Finite difference, Nonlinearity, Two-dimension

Kaynak

Engineering Analysis with Boundary Elements

WoS Q Değeri

Q1

Scopus Q Değeri

Q1

Cilt

129

Sayı

Künye

Oruç, Ö. (2021). A local radial basis function-finite difference (RBF-FD) method for solving 1D and 2D coupled Schrödinger-Boussinesq (SBq) equations. Engineering Analysis with Boundary Elements, 129, 55-66.