classical explicit finite difference schemes are unsuitable for the solution of the famous black-scholes partial differential equation, since they impose severe restrictions on the time step. furthermore, they may produce spurious oscillations in the solution. we propose a new scheme that is free of spurious oscillations and guarantees the positivity of the solution for arbitrary stepsizes. the...

Nowadays, numerical models have great importance in every field of science, especially for solving the nonlinear differential equations, partial differential equations, biochemical reactions, etc. The total time evolution of the reactant concentrations in the basic enzyme-substrate reaction is simulated by the Runge-Kutta of order four (RK4) and by nonstandard finite difference (NSFD) method. A...

‎In this paper we propose a numerical scheme to solve the one dimensional nonlinear Klein-Gorden equation‎. ‎We describe the mathematical formulation procedure in details‎. ‎The scheme is three level explicit and based on nonstandard finite difference‎. ‎It has nonlinear denominator function of the step sizes‎. ‎Stability analysis of the method has been given and we prove that the proposed meth...

In this paper, we present a new model using a Fourdimensional (4D) Element-Oriented physical concepts based on a topological approach in electromagnetism. Its general finite formulation on dual staggered grids reveals a flexible Finite-Difference Time-Domain (FDTD) method with reasonable local approximating functions. This flexible FDTD method is developed without recourse to the traditional Ta...

nonstandard finite difference schemes for the black-scholes partial differential equation preserving the positivity property are proposed. computationally simple schemes are derived by using a nonlocal approximation in the reaction term of the black-scholes equation. unlike the standard methods, the solutions of new proposed schemes are positive and free of the spurious oscillations.