We consider the fractional cable equation. For solution of fractional Cable equation involving Caputo fractional derivative, a new difference scheme is constructed based on Crank Nicholson difference scheme. We prove that the proposed method is unconditionally stable by using spectral stability technique.

The Burgers’ equation is a simplified form of the Navier-Stokes equations that very well represents their non-linear features. In this paper, numerical methods of the Adomian decomposition and the Modified Crank – Nicholson, used for solving the one-dimensional Burgers’ equation, have been compared. These numerical methods have also been compared with the analytical method. In contrast to...

In this paper, the groundwater flow equation is generalized using the concept of the variational order derivative. We present a numerical solution of the modified groundwater flow equation with the variational order derivative. We solve the generalized equation with the Crank-Nicholson technique. Numerical methods typically yield approximate solutions to the governing equation through the discr...

Variable-order fractional diffusion equation model is a recently developed and promising approach to characterize time-dependent or concentration-dependent anomalous diffusion, or diffusion process in inhomogeneous porous media. To further study the properties of variableorder time fractional subdiffusion equation models, the efficient numerical schemes are urgently needed. This paper investiga...

In this paper, a delayed Nicholson,s blowflies model with a linear harvesting term is investigated. Regarding the delay as a bifurcation parameter, we show that Hopf bifurcation will occur when the delay crosses a critical value. Numerical simulations supporting the theoretical findings are carried out. Keywords—Nicholson,s blowflies model; Stability; Hopf bifurcation; Delay.

This paper is concerned with the classical Nicholson-Bailey model [15] defined by fλ(x, y) = (y(1 − e−x), λye−x). We show that for λ = 1 a heteroclinic foliation exists and for λ > 1 global strict oscillations take place. The important phenomenon of delay of stability loss is established for a general class of discrete dynamical systems, and it is applied to the study of nonexistence of periodi...

s_an.nt.bz2 for Spanish and Aragonese, respectively. Available from https://github.com/jimregan/ es-an-sentences Table 1: Example first sentences from the Wikipedia articles “Mar”. es Un mar es una masa de agua salada de tamaño inferior al océano an A mar u o mar ye una masa d’augua salada de grandaria inferior a l’ocián A sea is a body of salt water smaller than an ocean Table 2: Example extra...

In this study, modifed Gauss elimination method will be used to obtain solution of first order Rothe difference scheme and second Crank-Nicholson for numerical approximation two-dimensional Schrödinger equation in space variable. One example is given approximate found by three methods. Modified with respect time variable compare the schemes are also solved classical inverse matrix method.

Blowflies are an important parasite of the sheep industry in countries like Australia. For the purposes of prevention, control and elimination, it is of interest to investigate both temporal and spatial variations of the blowflies population using mathematical models. Based on the experimental data of Nicholson [14, 15], Gurney et al . [5] established a dynamical model, the Nicholson blowflies ...