We made simulations of the collapse of the rotating protostellar cloud. Differential rotation leads to the amplification of the toroidal component of the magnetic field and subsequent ejection of the matter due to the magnetorotational mechanism.
Our results show that at different initial configurations of the magnetic field formation of qualitatively different types of explosion takes place. Magnetic field of the dipole type produces a jet-like explosion. Quadrupole-like magnetic field produces supernova explosion whith ejection presumably near equatorial plane. Quantitative estimations of the ejected mass and energy are given.
We have done simulation of the collapse of the white dwarf and formation of a differentially rotating neutron star. After the collapse stage the rotating neutron star was formed. The rotation of the neutron star is strongly differential. The presence of the magnetic field (even the weak one) could produce magnetorotational supernova explosion.
For the simulations we have used 2D numerical scheme, based on the specially developed numerical method (conservative, implicit, triangular grid, Lagrangian, grid reconstruction).