The invariant imbedding method for transport problems II. Resolvent in photon diffusion equation

An Algorithm for Solving Torsional Vibration Problems Based on the Invariant Imbedding Method

In this work the invariant imbedding method has been used to develop an algorithm to study the torsional vibration of non-uniform systems. The algorithm is based on the propagation, reflection, and transmission of waves in a stepped waveguide and is part of a procedure to transform two-point boundary value problems in initial value problems. Based on this approach, a continuous model has been d...

Generalized Invariant Imbedding Relation.

Effective source term in the diffusion equation for photon transport in turbid media.

The Green's function for the diffusion equation is widely used to describe photon transport in turbid media. We have performed aseries of spectroscopy experiments on a number of uniform turbid media with different optical properties (absorption coefficient in the range 0.03-0.14 cm(-1), reduced scattering coefficient in the range 5-22 cm(-1)). Our experiments have been conducted in the frequenc...

The streamline diffusion method with implicit integration for the multi-dimensional Fermi Pencil Beam equation

We derive error estimates in the appropriate norms, for the streamlinediffusion (SD) finite element methods for steady state, energy dependent,Fermi equation in three space dimensions. These estimates yield optimal convergencerates due to the maximal available regularity of the exact solution.High order SD method together with implicit integration are used. The formulationis strongly consistent...

Galerkin Method for the Numerical Solution of the Advection-Diffusion Equation by Using Exponential B-splines

In this paper, the exponential B-spline functions are used for the numerical solution of the advection-diffusion equation. Two numerical examples related to pure advection in a finitely long channel and the distribution of an initial Gaussian pulse are employed to illustrate the accuracy and the efficiency of the method. Obtained results are compared with some early studies.