The modern level of computing technologies makes it possible to perform the mathematical simulation of complicated scientific problems and to study a number of natural phenomena, such as the formation of stars and planetary systems from a protosubstance and their further evolution. One of the most efficient gas-dynamic computation methods for astrophysical simulation is the meshless smoothed particle hydrodynamics method (the SPH-method). The complete Lagrangian nature of this method allows one to conduct simulations over a very wide dynamic range of density, pressure, and temperature. A number of numerical results obtained by the SPH-method are discussed. In order to take into account the gravitation interactions, a hierarchical tree-code method is applied.

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