Before revision:  Furthermore, it is possible to further increase the accuracy of the solutions in 2D with a simple modification of the RFB method. We provide analysis to show how the modified-RFB method mitigates the pollution error. The analysis gave rise to a fourth order accurate finite difference scheme that uses seven-point stencil. The modified-RFB is able to solve the Helmholtz equation efficiently in 2D up to ch = 3.5 where c is the wave number and h is the mesh size  .
After revision:  Furthermore, it is possible to further increase the accuracy of the solutions in 2D with a simple modification of the sub-problems. This modification increases the accuracy of the numerical solution impressively. The AB method is able to solve the Helmholtz equation efficiently in 2D up to ch = 3.5 where c is the wave number and h is the mesh size .