In this work, we construct a fifth-order weighted essentially non-oscillatory (WENO) scheme with exponential approximation space for solving dispersive equations. A conservative third-order derivative formulation is developed directly using WENO spatial reconstruction procedure and third-order TVD Runge- Kutta scheme is used for the evaluation of time derivative. This exponential approximation space consists a tension parameter that may be optimized to fit the specific feature of the charecteristic data, yielding better results without spurious oscillations compared to the polynomial approximation space. A detailed formulation is presented for the the construction of conservative flux approximation, smoothness indicators, nonlinear weights and verified that the proposed scheme provides the required fifth convergence order. One and two-dimensional numerical examples are presented to support the theoretical claims.

翻译：本文构造了一种基于指数逼近空间的五阶加权本质无振荡（WENO）格式，用于求解色散方程。直接利用WENO空间重构过程发展了一种守恒型三阶导数公式，并采用三阶TVD Runge-Kutta格式进行时间导数的计算。该指数逼近空间包含一个张力参数，可针对特征数据的特定特征进行优化，相较于多项式逼近空间，能在无虚假振荡的情况下获得更优结果。本文详细给出了守恒通量逼近、光滑指示因子、非线性权重的构造公式，并验证了所提格式具有所需的五阶收敛精度。通过一维和二维数值算例支持了理论结论。