The numerical multidimensional approximation for the fast solving of equations describing charged particle motion in inhomogeneous magnetic fields

Some mathematical problems connected with the numerical solving of equations of motion for charged particles in inhomogeneous magnetic fields are considered. The three-dimensional spline approximation of the magnetic field is proposed. This allows one to use high-accuracy numerical methods to evaluate the trajectory of the moving charged particle in inhomogeneous magnetic field. On the base of multidimensional approximation the fast algorithms for the description of equations of motion solution and its derivatives with respect to initial data are proposed. The application of the considered methods for ALICE experiment are demonstrated.