A local radial basis function-finite difference (RBF-FD) method for solving 1D and 2D coupled Schrödinger-Boussinesq (SBq) equations
| Autor: | Ömer Oruç |
|---|---|
| Přispěvatelé: | Dicle Üniversitesi, Fen Fakültesi, Matematik Bölümü, Oruç, Ömer |
| Rok vydání: | 2021 |
| Předmět: |
Finite difference
Two-dimension Applied Mathematics General Engineering Basis function 02 engineering and technology Coupled Schrödinger-Boussinesq (SBq) equations 01 natural sciences 010101 applied mathematics Polyharmonic spline Computational Mathematics Runge–Kutta methods 020303 mechanical engineering & transports 0203 mechanical engineering Local meshless method Meshfree methods Applied mathematics Radial basis function 0101 mathematics Temporal discretization Spectral method Nonlinearity Analysis Mathematics |
| Zdroj: | Engineering Analysis with Boundary Elements. 129:55-66 |
| ISSN: | 0955-7997 |
| Popis: | 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 ∞ 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. |
| Databáze: | OpenAIRE |
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