Abstract. In this paper, a numerical solution for the system described by a generalized fractional Rikitake system is presented. The first step in the proposed procedure is represent the fractional order Rikitake system as an equivalent system of ordinary differential equations. In the second step, we solved the system obtained in the first step by using the well known fourth order Runge-Kutta ...

A method is presented to easily derive von Neumann stability conditions for a wide variety of time discretization schemes for the convection-di usion equation. Spatial discretization is by the -scheme or the fourth order central scheme. The use of the method is illustrated by application to multistep, Runge-Kutta and implicit-explicit methods, such as are in current use for ow computations, and...

Exponential Runge–Kutta methods constitute efficient integrators for semilinear stiff problems. So far, however, explicit exponential Runge–Kutta methods are available in the literature up to order 4 only. The aim of this paper is to construct a fifth-order method. For this purpose, we make use of a novel approach to derive the stiff order conditions for high-order exponential methods. This all...

In this paper, a fractional order HIV/AIDS (FOHA) epidemic model with treatment is investigated. The first step in the proposed procedure is represent the FOHA system as an equivalent system of ordinary differential equations. In the second step, we solved the system obtained in the first step by using the well known fourth order Runge-Kutta method. Numerical simulations are also presented to v...

Strong stability preserving (SSP) high order Runge–Kutta time discretizations were developed for use with semi-discrete method of lines approximations of hyperbolic partial differential equations, and have proven useful in many other applications. These high order time discretization methods preserve the strong stability properties of first order explicit Euler time stepping. In this paper we a...

‎In this paper‎, ‎the fractional--order form of three dimensional chemostat model with variable yields is introduced‎. ‎The stability analysis of this fractional system is discussed in detail‎. ‎In order to study the dynamic behaviours of the mentioned fractional system‎, ‎the well known nonstandard (NSFD) scheme is implemented‎. ‎The proposed NSFD scheme is compared with the forward Euler and ...

where y(x) denotes the solution of the differential equation. The idea is to use a quadrature formula to estimate the integral of (1). This requires knowledge of the integrand at specified arguments x¿ in (xo, -To + h)—hence we require the values of y(x) at these arguments. A numerical integration method may be used to estimate y(x) for the required arguments. In this way a numerical integratio...