AbstractA technique is described for solving the compressible flow equations in subsonic flow. The general quasi‐linear equation ∇.g∇v= 0 is considered withga function of ∇v. ∇v, and iterations of the form ∇.gn∇vn+1= 0 are analysed, whereg0is suitably chosen andgndefined fromvnforn≥1. This approach is applied to the compressible flow equations in terms of a velocity potential ø: monotonic convergence is predicted and at each iteration the error is multiplied by a factor less than the square of the greatest Mach number in the solution.Reliable convergence has been obtained in practice solving the linear equation for øn+1 by a finite difference method. The alternative of working in terms of the stream function ψ is discussed, and also discretization by the fin