A correct derivation of acceleration parameter for hopscotch and checkerboard (P, Q)-cyclic relaxation schemes

The correct method for applying the von Neumann stability analysis to composite finite difference schemes for numerical solution of partial differential equations is investigated. Our results provide justification of the hopscotch method and give correction to earlier analyses [1,7]. The methods employed here to analyze checkerboard and hopscotch iterative processes are also applicable to the study of more general composite (P, Q)-cyclic finite difference schemes.