طريقة الاتجاهات المتبادلة ضمنيا باستخدام الفروق النهائية المدمجة لحل معادلة الموجة

In this paper the Alternating Direction Implicit method ADI is studied using the idea of dividing the derivative for the time variable in the two-dimensional wave equation, where developed this method by approximating the second derivative for the space variable using the Compact finite difference of the fourth order and obtaining an algorithm of the fourth order for the space variable and the second order for the time variable, as well as both methods can be generalized to the three-dimensional wave equation, Finally we presented numerical examples where the results obtained were of good accuracy compared to the exact solution, and compared the results obtained with the results of the first and second Lazy methods and the generalized alternating direction implicit method .