Behavior of poroelastic isotropic beam derivation by asymptotic expansion method

Behavior of poroelastic isotropic beam derivation by asymptotic expansion method

Derivation of the Isotropic Diffusion Source Approximation (IDSA) for Supernova Neutrino Transport by Asymptotic Expansions

We present Chapman–Enskog and Hilbert expansions applied to the O(v/c) Boltzmann equation for the radiative transfer of neutrinos in core-collapse supernovae. Based on the Legendre expansion of the scattering kernel for the collision integral truncated after the second term, we derive the diffusion limit for the Boltzmann equation by truncation of Chapman–Enskog or Hilbert expansions with react...

Derivation of a Poroelastic Flexural Shell Model

In this paper we investigate the limit behavior of the solution to quasi-static Biot’s equations in thin poroelastic flexural shells as the thickness of the shell tends to zero and extend the results obtained for the poroelastic plate by Marciniak-Czochra and Mikelić in [16]. We choose Terzaghi’s time corresponding to the shell thickness and obtain the strong convergence of the three-dimensiona...

The Asymptotic Expansion Method via Symbolic Computation

The origin of symbolic manipulation derives from the sheer magnitude of the work involved in the building of perturbation theories, which made inevitable that scientific community became interested in the possibility of constructing those theories with the help of computers. Perturbation theories for differential equations containing a small parameter are quite old. The small perturbation theor...

Computation in an Asymptotic Expansion Method

An asymptotic expansion scheme in finance initiated by Kunitomo and Takahashi [15] and Yoshida[68] is a widely applicable methodology for analytic approximation of the expectation of a certain functional of diffusion processes. [46], [47] and [53] provide explicit formulas of conditional expectations necessary for the asymptotic expansion up to the third order. In general, the crucial step in p...