A new development of sixth order accurate compact scheme for the Helmholtz equation

A standard sixth order compact finite difference scheme for two dimensional Helmholtz equation is further improved and a more accurate scheme is presented for the two dimensional Helmholtz equation which is also compact. The novel feature of the present scheme is that it is less sensitive to the associated wave number when compared with that for available sixth order schemes. Theoretical analysis is presented for the newly constructed scheme. The high accuracy of the proposed scheme is illustrated by comparing numerical solutions for solving the two dimensional Helmholtz equations using available sixth-order schemes and the present scheme.