Numerical analysis of cubic orthogonal spline collocation methods for the coupled Schrodinger-Boussinesq equations

作者：Liao, Feng; Zhang, Luming; Wang, Shanshan^*

来源：Applied Numerical Mathematics, 2017, 119: 194-212.

DOI：10.1016/j.apnum.2017.04.007

• Orthogonal spline collocation
• Schrodinger-Boussinesq equations
• Conservation law
• Convergence
• Stability

In this article, we formulate two orthogonal spline collocation schemes, which consist of a nonlinear and a linear scheme for solving the coupled Schrodinger-Boussinesq equations numerically. Firstly, the conservation laws of our schemes are derived. Secondly, the existence solutions of our schemes are investigated. Thirdly, the convergence and stability of the nonlinear scheme are analyzed by means of discrete energy methods, while the convergence of the linear scheme is proved by cut-off function technique. Finally, numerical results are reported to verify our theoretical analysis for the numerical methods.

• 出版日期2017-9
• 单位南京航空航天大学