The time fourth-order compact ADI methods for solving two-dimensional nonlinear wave equations
The time fourth-order compact ADI methods for solving two-dimensional nonlinear wave equations
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DOI：
10.1016/j.amc.2018.02.010
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发表时间：
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期刊：
影响因子：
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通讯作者：
梁栋
中科院分区：
文献类型：
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作者：
邓定文;梁栋
Nonlinear wave equation is extensively applied in a wide variety of scientific fields, such as nonlinear optics, solid state physics and quantum field theory. In this paper, two high- performance compact alternating direction implicit (ADI) methods are developed for the nonlinear wave equations. The first scheme is developed a three-level nonlinear difference scheme for nonlinear wave equations, where in x -direction, series of linear tridiagonal sys- tems are solved by Thomas algorithm, while in y -direction, nonlinear algebraic system are computed by Newton’s iterative method. In contrast, the second scheme is linear, and per- mits the multiple uses of the Thomas algorithm in both x - and y -directions, thus it saves much time cost. By using the discrete energy analysis method, it is shown that both the developed schemes can attain numerical accuracy of order O(τ4 + h 4 x + h 4 y ) in H 1 -norm. Meanwhile, by the fixed point theorem and symmetric positive-definite properties of co- efficient matri x , it is proved that they are both uniquely solvable. Besides, the proposed schemes are extended to the numerical solutions of the coupled sine-Gordon wave equa- tions and damped wave equations. Finally, numerical results confirm the convergence or- ders and exhibit efficiency of our algorithms.
