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Invariant finite-difference schemes are considered for one-dimensionalmagnetohydrodynamics (MHD) equations in mass Lagrangian coordinates for thecases of finite and infinite conductivity. For construction these schemespreviously obtained results of the group classification of MHD equations areused.  On the basis of the classical Samarskiy-Popov scheme new schemes areconstructed for the case of finite conductivity. These schemes admit allsymmetries of the original differential model and have difference analogues ofall of its local differential conservation laws. Among the conservation lawsthere are previously unknown ones.  In the case of infinite conductivity, conservative invariant schemesconstructed as well. For isentropic flows of a polytropic gas proposed schemespossess the conservation law of energy and preserve entropy on two time layers.This is achieved by means of specially selected approximations for the equationof state of a polytropic gas. Also, invariant difference schemes withadditional conservation laws are proposed.  A new scheme for the case of finite conductivity is tested numerically forvarious boundary conditions which shows accurate preservation of differenceconservation laws.

Invariant finite-difference schemes with conservation laws preservation for one-dimensional MHD equations