Use of the method of parallel chords for solving difference equations of hydrodynamics

It is shown that the method of parallel chords, a modification of the Newton method, can be used to solve the difference equations of hydrodynamics, written in a Lagrangian form. Compared to the classical Newton method, the modified method has the following advantages: (1) single computation of the linear-system matrix makes it possible to reduce computations by one iteration; (2) matrix symmetry makes it possible to reduce the size of the memory; and (3) the positive and self-adjoint character of the linear-system operator removes several difficulties and reduces the time of solution of the system.