在本文中我們把複合介質中解線性雙曲線型偏微分方程的沈浸介面法推廣至更高階精確度。我們假設在所考慮的微分方程中，係數函數為片段常數函數。延續[8]一文中所用的方法，我們把複合介質中不連續面附近的有限差分方法，由二階提昇至四階精確度。經由在複合介質中光滑區段使用高階有限差分方法，如ENO-ROE法加以配合，所得的沈浸介面法證實針對複合介質中的波傳遞不需使用更細網格便可產生高解析度。

　　　　　We extend the immersed interface method for solving linear hyperbolic equations in heterogeneous media to higher order accuracy. The coefficient functions of the hyperbolic equations considered are assumed to be piecewise constant. We extend the treatment on each interface of discontinuity in [8] from second order accurate to fourth order accurate. By combining the resulting high order interface treatment with high order finite difference schemes, e.g. ENO-ROE schemes, for solving the hyperbolic equations in smooth regions, the resulting immersed interface method is capable of providing sharp resolution of the wave propagation on heterogeneous media without using very fine grids.