Geodesic
On lakuna based algorithm for numerical solution of 3D~-- wave equation for arbitrary great time
Matematičeskoe modelirovanie, Tome 11 (1999) no. 12, pp. 113-126.

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A numerical algorithm for 3D – wave equation Cauchy-problem is constructed. It is assumed the Cauchy-dates identically zero and right hand of wave-equation is zero outside of unit sphere. The domain to compute is bounded and fixed. The algorithm provides the solution during arbitrary long time with prestabileshed arbitrary exactness. The computer expenditures for one time-step progress are independet on time-step number and can't be decreased essentially. The lacuna of 3D – wave equation is used. The results can be used for calculations of acoustic, elastic and electromagnetic fields around local nonstationary sources. 
@article{MM_1999_11_12_a10,
     author = {V. S. Ryaben'kii and V. I. Turchaninov and S. V. Tsynkov},
     title = {On lakuna based algorithm for numerical solution of {3D~--} wave equation for arbitrary great time},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {113--126},
     publisher = {mathdoc},
     volume = {11},
     number = {12},
     year = {1999},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_1999_11_12_a10/}
}
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V. S. Ryaben'kii; V. I. Turchaninov; S. V. Tsynkov. On lakuna based algorithm for numerical solution of 3D~-- wave equation for arbitrary great time. Matematičeskoe modelirovanie, Tome 11 (1999) no. 12, pp. 113-126. http://geodesic.mathdoc.fr/item/MM_1999_11_12_a10/