The numerical simulation of the diffusive-like decay of the vortex tangle without mutual friction was performed. The simulation was made with the use of the localized induction approximation. The early developed by authors algorithm, which is based on consideration of crossing lines, was used for vortex reconnection processes. We have determined the influence of different factors on decay of an inhomogeneous vortex tangle: a diffusion (large vortex loops break up to smaller ones which go away from initial volume), change of length owing to reconnection processes, the eliminations of small vortices below the space resolution, the insertion and removing of points to supply numerical algorithm stability. The obtained numerical results demonstrate that the vortex tangle, initially localized in the small region, is smearing into ambient space. The time evolution of vortex line density inside the initial domain satisfactory agrees with the ones, obtained from the solution of diffusion equation.

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