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首页> 外文期刊>European Physical Journal Plus >Numerical simulation of solitary waves of Rosenau-KdV equation by Crank-Nicolson meshless spectral interpolation method
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Numerical simulation of solitary waves of Rosenau-KdV equation by Crank-Nicolson meshless spectral interpolation method

机译：曲柄 - 尼科尔森网状谱插值法测定罗森-KDV方程孤立波的数值模拟

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摘要

An efficient and accurate Crank-Nicolson meshless spectral radial point interpolation (CN-MSRPI) method is proposed for the numerical solution of nonlinear Rosenau-KdV equation. The proposed method uses meshless shape functions, owing Kronecker delta property, for approximation of spatial operator. Crank-Nicolson difference scheme is used for temporal operator approximation. Single solitary wave motion, interaction of double and triple solitary waves as well as generation of train of solitary waves from initial data are numerically simulated. Error analysis is made via computation of discrete L infinity, L2 and Lrms error norms. Efficiency of the proposed numerical scheme is assessed via variation of number of nodes N and time step-size tau. Two invariant quantities correspond to mass and energy are computed using the proposed method for further validation. Stability of the proposed method is discussed and verified computationally. Comparison of obtained results made with exact and existing results in the literature revealed the proposed CN-MSRPI method superiority.
机译：提出了一种高效且精确的曲柄 - 尼古尔森网谱径向点插值（CN-MSRPI）方法，用于非线性Rosenau-KDV方程的数值解。该方法采用无丝绒形状函数，欠克朗克特Δ属性，用于空间操作员的近似。曲柄 - 尼古尔森差分方案用于时间操作员近似。单次孤立波动，双孤波的相互作用以及来自初始数据的孤立波的产生的相互作用在数值上进行了数值模拟。通过计算离散L Infinity，L2和LRMS误差规范进行错误分析。通过节点N和时间梯度TAU的数量进行评估所提出的数值方案的效率。使用所提出的方法来计算两种不变的数量对应于质量和能量，以进行进一步验证。计算和验证所提出的方法的稳定性。在文献中具有精确和现有结果的获得结果的比较揭示了所提出的CN-MSRPI方法优势。

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