CAJ | 학술논문

本文主要讨论带非局部粘性项水波方程的数值方法。我们建立了一种求解这类粘性水波方程的数值方案。该方案有效解决了非局部粘性项与非线性项的离散问题。所提的格式包括对α阶分数阶项的2?α阶格式和对非线性项的线性化处理的混合格式。我们证明了这种格式是无条件稳定的，并得出线性Crank-Nicolson加2?α格式的收敛阶是O(?t 32+N 1?m)的结论。一系列的数值例子验证了理论证明的正确性。最后，我们用所提数值格式研究了粘性水波方程的渐近衰减率，并讨论了各种参数项对衰减率的影响。
본문주요토론대비국부점성항수파방정적수치방법。아문건립료일충구해저류점성수파방정적수치방안。해방안유효해결료비국부점성항여비선성항적리산문제。소제적격식포괄대α계분수계항적2?α계격식화대비선성항적선성화처리적혼합격식。아문증명료저충격식시무조건은정적，병득출선성Crank-Nicolson가2?α격식적수렴계시O(?t 32+N 1?m)적결론。일계렬적수치례자험증료이론증명적정학성。최후，아문용소제수치격식연구료점성수파방정적점근쇠감솔，병토론료각충삼수항대쇠감솔적영향。
we focus on the numerical investigation of a water wave model with a nonlocal vis-cous dispersive term. We construct and analyze a schema to numerically solving the nonlocal water wave model. The key for the success consists in a particular combination of the treatments for the nonlocal dispersive term and nonlinear convection term. The proposed methods employ a known (2?α)-order schema for the α-order fractional derivative and a mixed linearization of the nonlinear term. A rigorous analysis shows that the proposed schema is unconditionally stable, and the linearized Crank-Nicolson plus (2?α)–order schemes is O(?t 32 +N 1?m). A series of numerical examples is presented to confirm the theoretical prediction. Finally the proposed methods are used to investigate the asymptotical decay rate of the solutions of the nonlocal viscous wave equation, as well as the impact of different terms on this decay rate.