On application of compact schemes for solving the wave equation

A detailed comparison of one-dimensional compact schemes versus central-difference ones approximating the second derivative is done. The comparison criterion is based on computational costs required achieving a given accuracy. Low-cost algorithms for solving the wave equation with use of the highly-accurate compact schemes are proposed. The issues of accurate calculation by compact schemes of the second derivative near to boundaries, including a case of characteristic boundary conditions are considered. One of conclusions is that beginning from the 6th order of accuracy the compact schemes with the “three-point” left-hand-side operators are more effective than their central-difference counterparts.