Piecewise parabolic method on local stencil. III. 1D ideal MGD

Technique for solving of ideal MGD system of equations in 1D case with the help of piecewise parabolic method on local stencil (PPML) is suggested. This method is proposed by the authors modification of standard piecewise parabolic method (PPM). The modification is based on the property of Riemann invariants to conserve when moving along the characteristic curves of hyperbolic system of equations and improves the dissipative properties of PPM. Testing of PPML was carried out for some 1D test problems of ideal MGD.