In this work, a predictor–corrector compact difference scheme for nonlinear fractional differential equation is presented. The MacCormack method provided to deal with terms, the Riemann–Liouville (R-L) integral term treated by means of second-order convolution quadrature formula, and Caputo derivative discretized L1 discrete formula. Through first second derivatives matrix under difference, we ...

Let G be a d-regular graph with girth g, and let α be the independence number of G. We show that α(G) ≥ 12 ( 1− (d− 1)−2/(d−2) − (g) ) n where (g) → 0 as g → ∞, and we compute explicit bounds on (g) for small g. For large g this improves previous results for all d ≥ 7. The method is by analysis of a simple greedy algorithm which was motivated by the differential equation method used to bound in...

In this article we have considered Fredholm integro-differential equation type second-order boundary value problems and proposed a rational difference method for numerical solution of the problems. The composite trapezoidal quadrature and non-standard difference method are used to convert Fredholm integro-differential equation into a system of equations. The numerical results in experiment on s...

In system dynamics modeling, differential equations have been used as the basic mathematical operator. Using difference equation to build system dynamics models instead of differential equation, can be insightful for studying small organizations or systems with micro behavior. In this paper we explain how we can use difference equations to build system dynamics models. We illustrate the use of ...

We introduce the standard fourth order compact finite difference formulae. We show how these formulae apply in the special case of the heat equation. It is well known that the American option pricing problem may be formulated in terms of the Black Scholes partial differential equation (PDE) together with a free boundary condition. Standard methods allow this problem to be transformed into a mov...