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This article is in continuation of our earlier article [37] in which computational solution of an unified reaction-diffusion equation of distributed order associated with Caputo derivatives as the time-derivative and Riesz-Feller derivative…
For a model convection-diffusion problem, we address the presence of oscillatory discrete solutions, and study difficulties in recovering standard approximation results for its solution. We justify the presence of non-physical oscillations…
Invasion phenomena for heterogeneous reaction-diffusion equations are contemporary and challenging questions in applied mathematics. In this paper we are interested in the question of spreading for a reaction-diffusion equation when the…
The time-fractional convection-diffusion equation is performed by Lie symmetry analysis method which involves the Riemann-Liouville time-fractional derivative of the order $\alpha\in(0,2)$. In eight cases, the symmetries are obtained and…
The main result of this article establishes strong convergence rates on the whole probability space for explicit space-time discrete numerical approximations for a class of stochastic evolution equations with possibly non-globally monotone…
Differential equations are derived for a continuous limit of iterated Schwarzian reflection of analytic curves, and solutions are interpreted as geodesics in an infinite-dimensional symmetric space geometry.
We use a generic framework, namely the gradient discretisation method (GDM), to propose a unified numerical analysis for general time-dependent convection-diffusion-reaction models. We establish novel results for convergence rates of…
We model the evolution of the concentration field of macromolecules in a symmetric field-flow fractionation (FFF) channel by a one-dimensional advection-diffusion equation. The coefficients are precisely determined from the fluid dynamics.…
We construct a class of infinite mass functions for which solutions of the viscous Burgers equation decay at a better rate than solution of the heat equation for initial data in this class. In other words, we show an enhanced dissipation…
We construct a Convolution Quadrature (CQ) scheme for the quasilinear subdiffusion equation of order $\alpha$ and supply it with the fast and oblivious implementation. In particular, we find a condition for the CQ to be admissible and…
Analysis of the convergence rates of modern convex optimization algorithms can be achived through binary means: analysis of emperical convergence, or analysis of theoretical convergence. These two pathways of capturing information diverge…
Two-level domain decomposition preconditioners lead to fast convergence and scalability of iterative solvers. However, for highly heterogeneous problems, where the coefficient function is varying rapidly on several possibly non-separated…
In this article, we discuss the numerical solution of diffusion equations on random surfaces within the isogeometric framework. We describe in detail, how diffusion problems on random surfaces can be modelled and how quantities of interest…
This paper proposes a novel reaction-diffusion system approximation tailored for singular diffusion problems, typified by the fast diffusion equation. While such approximation methods have been successfully applied to degenerate parabolic…
The variable two-step backward differentiation formula (BDF2) is revisited via a new theoretical framework using the positive semi-definiteness of BDF2 convolution kernels and a class of orthogonal convolution kernels. We prove that, if the…
A space-time adaptive method is presented for the reactive Euler equations describing chemically reacting gas flow where a two species model is used for the chemistry. The governing equations are discretized with a finite volume method and…
Splitting methods constitute a well-established class of numerical schemes for solving convection-diffusion-reaction problems. They have been shown to be effective in solving problems with periodic boundary conditions. However, in the case…
We describe an exact and highly efficient numerical algorithm for solving a special but important class of convection-diffusion equations. These equations occur in many problems in physics, chemistry, or biology, and they are usually hard…
A new class of asynchronous discrete-event simulation schemes for advection-diffusion-reaction equations are introduced, which is based on the principle of allowing quanta of mass to pass through faces of a Cartesian finite volume grid. The…
This paper develops a two-level fourth-order scheme for solving time-fractional convection-diffusion-reaction equation with variable coefficients subjected to suitable initial and boundary conditions. The basis properties of the new…