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In this paper, we present error estimates of the integral deferred correction method constructed with stiffly accurate implicit Runge-Kutta methods with a nonsingular matrix $A$ in its Butcher table representation, when applied to stiff…
This paper examines the mathematical properties of the relativistic diffusion equation. The peculiar solution which Hiscock and Lindblom identified as an instability is shown to emerge from an ill-posed initial value problem. These do not…
Using theoretical and numerical arguments we discuss some of the commonly accepted approximations for the radiative transfer equations in climatology.
We describe our modelling of the radiatively cooling shocks and their thin shells with various numerical tools in different physical and calculational setups. We inspect structure of the dense shell, its formation and evolution, pointing…
An explicit numerical scheme is proposed for solving the initial-boundary value problem for the radiative transport equation in a rectangular domain with completely absorbing boundary condition. An upwind finite difference approximation is…
Stability of the kink-like and soliton-like travelling wave solutions to the generalized convection-reaction-diffusion equation is studied by means of the qualitative methods and numerical simulation.
Many important differential equations model quantities whose value must remain positive or stay in some bounded interval. These bounds may not be preserved when the model is solved numerically. We propose to ensure positivity or other…
We come back to the analytical solution of the standard transfer problem in a stellar atmosphere. It consists in solving the radiative transfer equation in a homogeneous and isothermal plane-parallel atmosphere, with light scattering taken…
We compare maps of scattering polarization signals obtained from three-dimensional (3D) radiation transfer calculations in a magneto-convection model of the solar atmosphere using formal solvers based on the "short characteristics" (SC) and…
We consider reaction-diffusion equations that are stochastically forced by a small multiplicative noise term. We show that spectrally stable travelling wave solutions to the deterministic system retain their orbital stability if the…
We consider the radiation transfer problem in the discrete-ordinate, plane-parallel approach. We introduce two benchmark problems with exact known solutions and show that for strongly non-homogeneous media the homogeneous layers…
This article presents an on-line tool (rttools.irap.omp.eu) and its accompanying software ressources for the numerical solution of basic radiation transfer out of local thermodynamic equilibrium (LTE). State-of-the-art stationary iterative…
The following document presents a possible solution and a brief stability analysis for a nonlinear system, which is obtained by studying the possibility of building a hybrid solar receiver; It is necessary to mention that the solution of…
In this work, we study the instability of an inverse problem of radiative transport equation with angularly averaged measurement near the diffusion limit, i.e. the normalized mean free path (the Knudsen number) $0 < \eps \ll 1$. It is…
This paper analyzes the stability of the class of Time-Accurate and Highly-Stable Explicit Runge-Kutta (TASE-RK) methods, introduced in 2021 by Bassenne et al. (J. Comput. Phys.) for the numerical solution of stiff Initial Value Problems…
We consider the radiative transfer problem in a plane-parallel slab of thermal electrons in the presence of an overcritical magnetic field. Under such conditions, the magnetic field behaves as a birefringent medium for the propagating…
A solution to a given equation is structurally stable if it suffers only an infinitesimal change when the equation (not the solution) is perturbed infinitesimally. We have found that structural stability can be used as a velocity selection…
When simulating resistive-capacitive circuits or electroquasistatic problems where conductors and insulators coexist, one observes that large time steps or low frequencies lead to numerical instabilities, which are related to the condition…
Solving the continuum radiative transfer equation in high opacity media requires sophisticated numerical tools. In order to test the reliability of such tools, we present a benchmark of radiative transfer codes in a 2D disc configuration.…
Modulation instability in a nonlinear optical waveguide array with alternating positive and negative refractive indices is investigated analytically. Particular solutions of a system of coupled nonlinear equations are found. These solutions…