We obtain cubature formulas of volume potentials over bounded domains combining the basis functions introduced in the theory of approximate approximations with their integration over the tangential-halfspace. Then the computation is reduced to the quadrature of one dimensional integrals over the halfline. We conclude the paper providing numerical tests which show that these formulas give very accurate approximations and confirm the predicted order of convergence. Bibliography: 6 titles. © 2013 Springer Science+Business Media New York.
Computation of volume potentials over bounded domains via approximate approximations / Lanzara, Flavia; V. G., Maz'Ya; G., Schmidt. - In: JOURNAL OF MATHEMATICAL SCIENCES. - ISSN 1072-3374. - STAMPA. - 189:3(2013), pp. 508-524. [10.1007/s10958-013-1203-2]
Computation of volume potentials over bounded domains via approximate approximations
LANZARA, Flavia;
2013
Abstract
We obtain cubature formulas of volume potentials over bounded domains combining the basis functions introduced in the theory of approximate approximations with their integration over the tangential-halfspace. Then the computation is reduced to the quadrature of one dimensional integrals over the halfline. We conclude the paper providing numerical tests which show that these formulas give very accurate approximations and confirm the predicted order of convergence. Bibliography: 6 titles. © 2013 Springer Science+Business Media New York.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.