The numerical solution of boundary value problems for ordinary differential equations on infinite intervals is considered. The infinite interval is cut at a finite, large enough point and additional boundary conditions are posed there. For the solution of the resulting problem, /(-stable symmetric collocation methods are employed. Using the behavior of the solution of the "infinite" problem, me...

Infinite product formulae for conformally mapping an unbounded multiply connected circle domain to an unbounded canonical radial or circular slit domain, or to domains with both radial and circular slit boundary components are derived and implemented numerically and graphically. The formulae are generated by analytic continuation with the reflection principle. Convergence of the infinite produc...

Mathematical models for pollutant transport in semi-infinite aquifers are based on the advection-dispersion equation (ADE) and its variants. This study employs the ADE incorporating time-dependent dispersion and velocity and space-time dependent source and sink, expressed by one function. The dispersion theory allows mechanical dispersion to be directly proportional to seepage velocity. Initial...

This paper presents a finite element-infinite element coupling approach for modeling a spherically symmetric transient flow problem in a porous medium of infinite extent. A finite element model is used to examine the flow potential distribution in a truncated bounded region close to the spherical cavity. In order to give an appropriate artificial boundary condition at the truncated boundary, a ...

Mathematical models for pollutant transport in semi-infinite aquifers are based on the advection-dispersion equation (ADE) and its variants. This study employs the ADE incorporating time-dependent dispersion and velocity and space-time dependent source and sink, expressed by one function. The dispersion theory allows mechanical dispersion to be directly proportional to seepage velocity. Initial...

The classification results for the extreme characters of two basic “big” groups, the infinite symmetric group S(∞) and the infinite-dimensional unitary group U(∞), are remarkably similar. It does not seem to be possible to explain this phenomenon using a suitable extension of the Schur-Weyl duality to infinite dimension. We suggest an explanation of a different nature that does not have analogs...

A formally exact effective boundary potential is defined that can be combined with hard-wall boundary conditions to allow computer simulations to be performed that mimic an infinite system. The effective potential accounts for the interactions that would be present across the boundary if the system were truly infinite. The exact many-body potential is approximated by oneand two-body potentials....