In this work we derive NonStandard Finite Differences (NSFDs)(Anguelov and Lubuma,
2001; Mickens, 2020) numerical schemes to solve a model consisting of reaction–diffusion …

In this paper a general class of diffusion problem is considered, where the standard time
derivative is replaced by a fractional one. For the numerical solution, a mixed method is …

The paper presents an adapted numerical integration for advection–reaction–diffusion
problems. The numerical scheme, exploiting the a-priori knowledge of the qualitative …

The paper is devoted to the numerical solution of advection–diffusion problems of
Boussinesq type, by means of adapted numerical methods. The adaptation occurs at two …

This paper concerns the construction of a general class of exponentially fitted two-step
implicit peer methods for the numerical integration of Ordinary Differential Equations (ODEs) …

In this paper, we present a general class of exponentially fitted two-step peer methods for
the numerical integration of ordinary differential equations. The numerical scheme is …

The numerical solution of reaction–diffusion equations of λ–ω type, which are known to
possess a one-parameter family of periodic plane wave solutions, is object of this paper …

In this paper, we use the method of lines to convert elliptic and hyperbolic partial differential
equations (PDEs) into systems of boundary value problems and initial value problems in …

Abstract Modified Gauss–Laguerre exponentially fitted quadrature rules are introduced for
the computation of integrals of oscillatory functions over the whole positive semiaxis. Their …

In this paper a new data assimilation technique is proposed which is based on the ensemble
Kalman filter (EnKF). Such a technique will be effective if few observations of a dynamical …