Nonstandard Dirac equations for nonstandard spinors

Nonstandard finite difference schemes for differential equations

In this paper, the reorganization of the denominator of the discrete derivative and nonlocal approximation of nonlinear terms are used in the design of nonstandard finite difference schemes (NSFDs). Numerical examples confirming then efficiency of schemes, for some differential equations are provided. In order to illustrate the accuracy of the new NSFDs, the numerical results are compared with ...

nonstandard finite difference schemes for differential equations

in this paper, the reorganization of the denominator of the discrete derivative and nonlocal approximation of nonlinear terms are used in the design of nonstandard finite difference schemes (nsfds). numerical examples confirming then efficiency of schemes, for some differential equations are provided. in order toillustrate the accuracy of the new nsfds, the numerical results are compared with s...

Elliptic and Parabolic Equations with Nonstandard Nonlinearity

• Mikhail Surnachev, Keldish Institute of Applied Mathematics Moscow Parabolic Equations Degenerating on a Part of the Domain ABSTRACT. In this work we study nonlinear parabolic equations of the p-Laplace type degenerating on a part of the domain. The degeneration is controlled by a small parameter. For the fixed value of this parameter, the results we discuss fall within the scope of E. DiBene...

Positivity-preserving nonstandard finite difference Schemes for simulation of advection-diffusion reaction equations

Systems in which reaction terms are coupled to diffusion and advection transports arise in a wide range of chemical engineering applications, physics, biology and environmental. In these cases, the components of the unknown can denote concentrations or population sizes which represent quantities and they need to remain positive. Classical finite difference schemes may produce numerical drawback...

FOUNDATIONS OF NONSTANDARD ANALYSIS A Gentle Introduction to Nonstandard Extensions