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.

In this paper, a mathematical model of Visceral Leishmaniasis is considered. The incorporates three populations, the human, reservoir and vector host populations. A detailed analysis presented. This reveals that undergoes backward bifurcation when associated reproduction threshold less than unity. For case where death rate due to VL negligible, disease-free equilibrium shown be globally-asympto...

We give an error estimate for the Energy and Helicity Preserving Scheme (EHPS) in second order finite difference setting on axisymmetric incompressible flows with swirling velocity. This is accomplished by a weighted energy estimate, along with careful and nonstandard local truncation error analysis near the geometric singularity and a far field decay estimate for the stream function. A key ing...

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. ©...

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.

In this paper, we consider an SIR-model for which the interaction term is the square root of the susceptible and infected individuals in the form of fractional order differential equations. First the non-negative solution of the model in fractional order is presented. Then the local stability analysis of the model in fractional order is discussed. Finally, the general solutions are presented an...