We point out a formal analogy between the Dirac equation in Majorana form and the discrete-velocity version of the Boltzmann kinetic equation. By a systematic analysis based on the theory of operator splitting, this analogy is shown to turn into a concrete and efficient computational method, providing a unified treatment of relativistic and nonrelativistic quantum mechanics.

The paper examines a particular class of nonlinear integro-differential equations consisting of a Sturm-Liouville boundary value problem on the half-line, where the coefficient of the differential term depends on the unknown function by means of a scalar integral operator. In order to handle the nonlinearity of the problem, we consider a fixed point iteration procedure, which is based on considering a sequence of classical Sturm-Liouville boundary value problems in the weak solution sense.

We consider a particular second-order integrodifferential boundary value problem arising from the kinetic theory of dusty plasmas, and we provide information on the existence and other qualitative properties of the solution that have been essential in the numerical investigation.

An algorithm for coupling SPH with an external solution is presented. The external solution can be either another SPH solution (possibly with different discretization) or a different numerical solver or an analytical solution. The interaction between the SPH solver and the external solution is achieved through an interface region. The interface region is defined as a fixed portion of the computational domain that provides a boundary condition for the SPH solver. A ghost fluid, composed by fully lagrangian particles (i.e.