Estimation of internal source distributions using external field measurements in radiative transfer

Intensity of emergent radiation for finite homogeneous slab which absorbs radiation and scatters it isotropicall

Numerical estimation of derivatives with an application to radiative transfer in spherical shells

Numerical estimation of derivatives with application to radiative transfer in spherical shell

Invariant imbedding and perturbation techniques applied to diffuse reflection from spherical shells

Invariant imbedding and perturbation techniques applied to diffuse reflection from spherical shell

The invariant imbedding equation for the dissipation function of a homogeneous finite slab

Differential-integral equation for dissipation function and derivation of conservation relationship connecting reflection, transmission and dissipation functions of finite sla

Analytic calculation of energies and wave functions of the quartic and pure quartic oscillators

Ground state energies and wave functions of quartic and pure quartic oscillators are calculated by first casting the Schr\"{o}dinger equation into a nonlinear Riccati form and then solving that nonlinear equation analytically in the first iteration of the quasilinearization method (QLM). In the QLM the nonlinear differential equation is solved by approximating the nonlinear terms by a sequence of linear expressions. The QLM is iterative but not perturbative and gives stable solutions to nonlinear problems without depending on the existence of a smallness parameter. Our explicit analytic results are then compared with exact numerical and also with WKB solutions and it is found that our ground state wave functions, using a range of small to large coupling constants, yield a precision of between 0.1 and 1 percent and are more accurate than WKB solutions by two to three orders of magnitude. In addition, our QLM wave functions are devoid of unphysical turning point singularities and thus allow one to make analytical estimates of how variation of the oscillator parameters affects physical systems that can be described by the quartic and pure quartic oscillators.Comment: 8 pages, 12 figures, 1 tabl

Quasilinearization Method and Summation of the WKB Series

Solutions obtained by the quasilinearization method (QLM) are compared with the WKB solutions. Expansion of the $p$-th QLM iterate in powers of $\hbar$ reproduces the structure of the WKB series generating an infinite number of the WKB terms with the first $2^p$ terms reproduced exactly. The QLM quantization condition leads to exact energies for the P\"{o}schl-Teller, Hulthen, Hylleraas, Morse, Eckart potentials etc. For other, more complicated potentials the first QLM iterate, given by the closed analytic expression, is extremely accurate. The iterates converge very fast. The sixth iterate of the energy for the anharmonic oscillator and for the two-body Coulomb Dirac equation has an accuracy of 20 significant figures

Nonlocal Automated Comparative Static Analysis

This paper reviews work on the development of a program Nasa for the automated comparative static analysis of parameterized nonlinear systems over parameter intervals. Nasa incorporates a fast and efficient algorithm Feed for the automatic evaluation of higher-order partial derivatives, as well as an adaptive homotopy continuation algorithm for obtaining all required initial conditions. Applications are envisioned for fields such as economics where models tend to be complex and closed-form solutions are difficult to obtain