A local radial basis function-finite difference (RBF-FD) method for solving 1D and 2D coupled Schrödinger-Boussinesq (SBq) equations. (1st August 2021)

• Record Type: Journal Article
• Authors: Oruç, Ömer
• Is Part Of: Engineering analysis with boundary elements. Volume 129(2021)
• Page Start: 55
• Page End: 66
• Publication Date: 2021-08-01
• Subjects: Coupled Schrödinger-Boussinesq (SBq) equations -- Local meshless method -- Finite difference -- Nonlinearity -- Two-dimension; Boundary element methods -- Periodicals; Engineering mathematics -- Periodicals; Équations intégrales de frontière, Méthodes des -- Périodiques; Mathématiques de l'ingénieur -- Périodiques; Boundary element methods; Engineering mathematics; Periodicals; 620.00151
• DOI: 10.1016/j.enganabound.2021.04.019
• Languages: English
• ISSNs: 0955-7997

Abstract

Abstract: In this study, one-dimensional (1D) and two-dimensional (2D) coupled Schrödinger-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 ∞ 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.