In this paper, the Black–Scholes equation is solved using a new technique. This scheme derived by combining Laplace transform method and nonstandard finite difference (NSFD) strategy. The qualitative properties of are discussed, it shown that positive, stable, consistent when low volatility assumed. efficiency demonstrated numerical example.

Let Λ be a discretly ordered abelian group. In that event the positive class N of the ordred abelian group Z embeds in the positve class Λ+ of Λ as an initial segment. If A is any nonempty set and λ is any positive element of Λ, then by an infinite word (of length λ) on the alphabet A is meant a function from the intial segment [1, λ] = {x ∈ Λ : 1 ≤ x ≤ λ} of Λ+ into A. A.G. Myasnikov suggested...

The aim of this work is to present a nonstandard linear finite element method for a planar elasticity problem. The error for the solution computed with this method is estimated with respect to H 1 ×H 1-norm and second-order convergence is shown.  2001 IMACS. Published by Elsevier Science B.V. All rights reserved.

The union of every point-finite, completely measurable family of Loeb nullsets is itself a Loeb nullset, provided the nonstandard model satisfies a simple set-theoretic condition. One application of this result is that every Loeb measurable function into a metric space has a lifting.

In this work, a high resolution nonstandard finite-difference time-domain method for the transverse magnetic (TM) mode of 2D-Maxwell’s equations is derived. Stability and convergence analysis and numerical studies are presented for the proposed method. The accuracy of this numerical scheme is validated by simulating a light scattering cross-section by a perfectly-conducting circular cylinder. ©...

We discuss a new approach for the construction of the secondlevel Neumann-Neumann coarse space. Our method is based on an inexpensive and parallel analysis of the lower part spectrum of each subdomain stiffness matrix. We show that the method is flexible enough to converge fast on nonstandard decompositions and various types of finite elements used in structural analysis packages.

This paper brings together two methods producing numerical solutions with a statement of their quality — the nonstandard finite difference method and the method of validated computing. It deals with the construction and the analysis of reliable numerical discretizations of dynamical systems by employing these two techniques. An epidemiological model is used as a model example for their combined...

General multi-dimensional autonomous dynamical systems and their numerical discretizations are considered. Nonstandard stability-preserving finite-difference schemes based on the θ-methods and the second-order RungeKutta methods are designed and analyzed. Their elementary stability is established theoretically and is also supported by a set of numerical examples.

Three numerical methods have been used to solve the one-dimensional advection-diffusion equation with constant coefficients. This partial differential equation is dissipative but not dispersive. We consider the Lax-Wendroff scheme which is explicit, the Crank-Nicolson scheme which is implicit, and a nonstandard finite difference scheme (Mickens 1991). We solve a 1D numerical experiment with spe...

On a nonstandard two-parametric quantum algebra and its connections with U p,q (gl(2)) and U p,q (gl(1|1)) Abstract. A quantum algebra U p,q (ζ, H, X ±) associated with a nonstandard R-matrix with two deformation parameters(p, q) is studied and, in particular, its universal R-matrix is derived using Reshetikhin's method. Explicit construction of the (p, q)-dependent nonstandard R-matrix is obta...